I'd hardly say cats are social.
I don't think they're social in the wild state. They're considered solitary animals. But now that we've brought them into our homes, they're quite sociable with us. My cats were. And mine were sociable with each other...the ones in our family. Even their meow is thought to have developed only on account of living with humans.
Dogs are social also, but many people, myself included don't believe them to be
true pack animals in most situations. The terms "social" and "pack" are not the same thing. An animal can be social but not operate in a fully functioning pack.
Cats are serious hunters..obligate carnivores. They hunt more than they scavange. Dogs scavange more than they hunt and although carnivores (by their systems), behaviorally they are omnivores. That too, is controversial, but that is my take on it.
How they are different in those ways however, is pretty irrelevant to this debate as to whether they should be kept safe from roaming. In that way dogs and cats are the same. They are both potentially at risk and they both can potentially cause a lot of trouble.
How they are different is that it's easier to train a dog to stay in the yard (albeit very generally speaking) and harder to train a cat to stay in the yard. And that's due to their being different in that way....the way they are connected to humans going way back and their very natures. I just think if a cat can be positively kept in his own yard and positively doesn't kill birds and positively doesn't get eaten by some predator, or hurt by another human, then fine. But I don't believe that is ever a sure fire thing. Of course, on the other hand, I go hiking in the woods with my dogs and it's not a sure fire, positive thing that some bear or moose isn't going to sneak up on us and get us all. I understand the idea of benefits and quality of life being weighed against the risks. But there again, I see more of a need for dogs to get out and run in a relatively safe situation than I do for cats needing to be outside. And that's because I've seen cats have a rip roaring good time climbing and playing on those big, elaborate platform things with carpet all over and those swinging, dangling toys that hang off to swat at. They make all kinds of nifty toys and faux "prey" things for cats to enjoy. Then it's next to their human on the couch or lounging in front of a fire. All this is enough for cats IMO. (my opinion now. I didn't always think this way)
Dogs, on the other hand need more exercise than that generally, more training which requires seeing more novel things, more variety of environments, more humans and other dogs....basically, more socializing to become adapted to our human culture and environment and to become what they have been designed by evolution to become to humans....our relationship with them, the many jobs they do etc. They need that to be safe and pleasant members in our society.
Cats need soialization too, but since they don't have those same needs which come from going so many places with
US, herding sheep, being guides for disabled people, retrieving for hunters, protection and all the multitude of jobs out there, that socialization can be more limited...IN THE HOME and maybe with the addition of the vet's office or a couple of other places you might need to take your cat. In fact, if a kitten is kept from going outside, he does not habituate to the outside and therefore rarely even wants to go outside. Some may be more curious than others. But the way it works in
all animals is that during that critical early socialization period, what they don't experience, later...they won't want to experience. In other words, they've gotten along fine without it so far. There's curiosity and there's caution. After that critical socialization window closes, caution is the default setting. If it weren't true, wild animals would not be afraid of anything. A false positive with something they're initially curious about can wind up killing them. Then they can't pass on their curious genes because they're dead. So, keeping a kitten inside in the first place, never letting him venture out at all, normally keeps them happy and safe indoors.