OK, firstly, I like both cats and dogs. I've had a dog, and I hope to get another someday. I do prefer cats, but dogs are fine pets as well. But many people who have only ever had dogs and not cats seem to have a lot of misconceptions about what cats are like. So I'm going to talk about some of the common ones I've seen, and what the reality is.
Cats Are Aloof
My kitten follows me around the house, always wanting to be in the same room as me. As soon as I get up in the morning, she runs to greet me - sometimes wanting breakfast, but other times just wanting to play. Both of my cats regularly come up and jump on my lap to cuddle with me. And most nights, my cats sleep with members of the family - me or my parents. If I start crying, my older cat often makes a concerned meow and runs up to comfort me.
Cats love the humans they trust, and can be very affectionate towards them. Some of my cats have easily been as sociable towards me as my Lab cross was. Others were less sociable, but still made it very clear that they cared about me. The only cat I had who genuinely did not enjoy human company was a feral cat - and feral dogs don't like humans either. If properly socialized, either species can be a loving, affectionate pet. Cats are a bit less sociable, on average, but they are still quite sociable.
There is one big difference, though. Most dogs love strangers. They seem to see a stranger as 'a friend I haven't met yet'. I have met a few shy dogs, but the majority of dogs greet strangers with a wagging tail and excited panting. In contrast, most cats are shy around strangers. Cats in general are a lot more cautious than dogs - they're small animals and they know it. In many places, wolves are top predators. When they aren't, they have only a few challengers. In contrast, wildcats are small predators, who are often killed by larger predators. While dogs expect that they're safe as long as they're with their pack, cats need time to get used to the situation and figure out for themselves if it's safe.
What this means is that if you visit the home of a cat for the first time, many of them won't run up and greet you. They may hide, to the point where it's possible to visit a cat owner's home and not even realize they have a cat. If they don't hide, they'll probably seek out a safe spot to observe you at a distance, often somewhere up high. If you visit on a regular basis, the cat will warm up, especially if they sense that you like cats. Even then, many cats won't greet you the way they'd greet their owners, and they won't greet their owners that way in front of you. But that doesn't mean they aren't greeting xim excitedly when xe comes home alone, or when xe wakes up in the morning.
So, cats are aloof to strangers. But to the people they love, they're friendly and affectionate.
Cats Are Dominant Over Humans
When a dog is dominant over a human in the household, this is a serious problem. Dominant dogs act like bullies - possessive, aggressive and controlling. If they're a big dog, a dominance problem can get downright scary. Dog owners learn to take dominance seriously, and claim early so there's no misunderstanding.
Cats don't have this kind of dominance hierarchy. In multi-cat households, cats will often (but not always) form a dominance hierarchy. But it's more about who owns certain territories, rather than a generalized 'who is the boss'. One cat may be dominant in the kitchen, but subordinate in the human's bedroom. My older cat is dominant downstairs, but upstairs is the kitten's domain, and she's rarely seen there.
With that said, most cats accept that humans are dominant over them. But they'll still set boundaries and object if these are crossed. Meanwhile, if your cat is dominant over you, that doesn't mean they won't respect your boundaries, if you communicate them in a proper cat fashion. Cats can be trained, though they're less eager about it than dogs are.
A couple of times, my Lab cross let us do things to her that we're pretty sure caused her physical pain. My Dad once cleaned out an infected wound on her stomach, and in the process discovered that our dog had a serious problem which turned out to be cancer. The cancer was so painful she'd bitten herself to try to make it stop. I have no doubt that my Dad poking around in there to clean it hurt the dog quite a bit. But she didn't complain, just stood there bravely and let him do it.
This kind of behaviour is fairly common among dogs. I've known of abused dogs who still came to their owners even knowing they'd be abused. I have only ever known one cat, an exceptionally submissive cat, who would let a human hurt him. (He had undiagnosed oral cancer and I was brushing his chin and accidentally hit him in the jaw with the brush. He didn't try to get away or stop me from continuing brushing, to the point where I didn't even realize it had hurt him. Only later, once he was diagnosed, did I realize how painful that must have been.) This cat was unusual - most cats, even if they see you as the boss in most things, will fight vigorously if you're causing them pain. It's one of the things I like about cats - they generally tell you what they don't like. My Lab cross wouldn't dare tell a dominant she didn't like something. Instead she'd just look pitiful and hope you stopped soon.
I've heard people say that cats think of humans as servants. That's certainly not how my cats think of me. My older cat, the one who comforts me when I'm crying, sees me as her kitten. I know because she makes the exact same sound when I'm crying that a mother cat makes when she hears a kitten crying. As for my kitten, I'm pretty sure she sees me as a playmate.
Both of them will ask me to do things for them, with my clever human hands, but then so will dogs. It's only practical, if you know you can't do something and someone you trust can, to ask them for help. And both cats and dogs, if not answered, will persist in asking for quite awhile before giving up. It means nothing for how they generally think of you - all it means is that they want help and know you can give it.
Cats Are Solitary
Cats used to be solitary. The Egyptian Wildcat, the species all domestic cats descend from, typically avoids other members of their species, using scent and urine marking to signal where they are and avoiding fresh scent and urine marks made by others. They need to avoid places hunted by other cats, or else they won't find enough prey and they'll starve.
But when humans started storing large amounts of grain, and consequently attracting large amounts of rodents, food was so plentiful that hundreds of cats could share the same territory without going hungry. And cats had to adapt, or be driven out of these plentiful places by hordes of intruders. The cats who stayed in human settlements were the most tolerant of other cats, and over the generations, many of them came to actually enjoy the company of other cats.
Now, if left to go feral, many cats will not live solitary lives. Females will seek out other females to raise their kittens together, and males will tolerate each other and form friendships. Cats have even developed a whole new communicative signal, not seen in any other feline species - the 'tail up' signal, used by a cat approaching a more powerful cat with a non-aggressive intention. (Cats also use this signal a lot with humans.)
What this means is that cats are adaptable. They can handle being alone, and they can enjoy having company. If you want to have only one cat, you don't need to worry about getting them contact with other cats. But if you have more than one cat, they can learn to enjoy each other's company (as long as introductions are handled well) and once they've come to be friends, they will seek each other out for cuddles and play. Kittens especially seem to crave social interaction - after all, even Egyptian Wildcats are sociable in kittenhood.
Cats Are Mean/Attack For No Reason
Well, firstly, it's important to know that no animal ever attacks for no reason. Every behaviour has a reason. You just need to figure out what it is.
Both cats and dogs will sometimes attack playfully. A universal behavioural trait among Carnivorans (the family of animals that includes cats and dogs, as well as bears, skunks, weasels, raccoons and many other animals) is the 'inhibited bite'. This is a gentle bite that never breaks the skin and hurts only a little, used by these animals as a play signal, and both puppies and kittens will happily give inhibited bites to humans.
In dogs, it's recommended to train them out of giving play bites to humans. Partly because a full-grown, medium to large dog can easily misjudge the strength of their jaws and bite too hard, and partly because not tolerating being bitten gives a clear signal to your dog that you're dominant over them. Puppy play fighting gradually evolves into asserting dominance, and it's important that the human be on the winning side of these fights from the very beginning.
In cats, as I said above, dominance doesn't matter as much. Both dominant and submissive cats will readily play bite each other, as well as play clawing. And since an adult cat doesn't get very big, their play bites are never going to be very painful (though adult cats rarely play bite anyway). So it's more a matter of preference, whether you want to train your cats never to treat humans as toys, or whether you'll put up with some scratching and biting for the fun of luring your kittens with your fingers. If you don't want them using you as a toy, you teach them by using objects as toys and by stopping play whenever they hurt you - same as with a puppy. Never reward them for biting or scratching, and don't retaliate (this will either be seen as you playing back, or make them think they have to defend themselves by fighting for real).
Cats also show defensive aggression. Since cats are more cautious than dogs, it's easier to overwhelm or scare a cat. And since cats are more assertive (even submissive cats), they're more likely to fight back if they feel threatened.
There are some things that dogs like and cats hate. Probably the biggest one is belly scrubbing. I've known a few male cats who enjoyed a good belly scrubbing, but most males, and all females, get mad if you touch their belly. And just because a cat shows you their belly doesn't mean they want it touched. Some cats just roll over from excitement, then get back up for more petting. And a submissive, defensive cat will sometimes roll onto their side to free up their paws for defending themselves. (If the cat's ears are back and they're staring at you intently, they are feeling defensive, and will attack if you touch their belly.) Cats also tend to get annoyed if you touch their tail, or sometimes their paws.
Being cradled on their back is something a cat will only tolerate if they're extremely trusting of you. Most cats get nervous being in such a helpless position, and will struggle and possibly even attack if you don't release them. Many dogs don't like this either, but generally only small dogs are put in this position.
Incidentally, there is also something I've found that cats love, and dogs generally don't - throat stroking. If you stroke a cat's throat, the usual reaction is a look of bliss, and stretching out their head to make it easier for you to reach just the right spot. But if you stroke a dog's throat, you can trigger their gag reflex. In the wild, canines often regurgitate food for their puppies, and puppies request this by licking their throat. Felines just carry prey in their mouths.
And cats nearly always warn before attacking. Many people really don't know how to read a cat's body language, so they think a cat's happy when they are actually getting annoyed. If a cat is flicking their ears back, twitching their tail vigorously, or staring at you with wide-open eyes and huge pupils, they're giving you warning signs. Cats will also back away, or lower their body as you try to pet their back, and those signals also mean 'leave me be'. And if a cat is staring at you with one of their front paws held up off the ground, they're ready to swat you. (Some of these signals can also be seen in a playful cat. But a playful cat will have a relaxed body, and if ignored, they will try to entice you back into interaction. An unhappy cat will be tense, and if ignored they will gradually calm down.)
Whereas if a cat is slowly blinking at you or looking at you through half-closed eyes, they are relaxed and happy. And if they enjoy you petting them, they will lean into the petting, close their eyes, and sometimes even get a slight little smile on their face. Cats also ask for petting by rubbing their body against you or bumping you with their head.
Cats have very sensitive skin. Each strand of fur has touch sensors wrapped around its' base, and cats can even feel vibrations in the air from something moving nearby them. Rough, vigorous petting, or petting in certain spots, will overwhelm and threaten them. But gentle, repetitive strokes on the right spots are utter bliss for them, and they will tell you this clearly.
If you get a cat really happy, they will start to purr. And not only is this one of the most wonderful sounds I can imagine, but new research suggests it can actually strengthen your bones