I've certainly seen people keep pet alligators around the house, though I'm not sure if any genuine bonding had happened or if the gators were just plain well-fed and aware that the human didn't pose a threat.
But you can certainly rear pretty much any mammal and many birds to treat a human as a family member. The important thing is to hand-raise them from a VERY young age, minimise contact with their own species, and maintain the relationship every few days at least (ideally daily). You alternate between being a parent and sibling figure.
Things get trickier with social animals (like the raptors, or in the real world, lions and wolves) which need to maintain a group hierarchy and might see the human as a rival if he or she isn't incredibly careful.
There's also the constant problem that a large animal can main or kill you without intending or even trying. Rhino calves love to charge around the place indiscriminately, putting you in real danger once they're heavier than you are. Big cats smack each other around just to play or even as a display of affection. Wolves and hyenas are constantly biting each other as standard social behaviour. If an adult bear sits on you then you're in trouble. Some male animals become uncontrollably aggressive when they're horny. Then there's the issue that any animal can lash out unpredictably if it's sick, injured or pregnant.
So you can form a perfect bond with a large animal and still be in mortal danger every time you interact with it. That's why it's not commonly done - but it's definitely possible, at least in species with highly developed child rearing behaviour.
