You've raised generations of cats and never had a kitten cut you up? Bullshit, your memory is shot. Sounds like you raised generations of inbred retards, real cats don't do that.
It's not a matter of socialization, reread what I wrote. They're not attacking, it's the way they play. Unfortunately we don't have fur to absorb most of those sharp little claws and teeth. They scream at each other when play gets too rough, and will stop if you scream too, but by the time they realize playtime is over the damage is done.
They can do a lot of damage in milliseconds. Sundae knows, so does Fargon, and Gravdigr.
Some dogs can purr.