That being said, I have worked with and met numerous Bully breeds in all of the work I do with shelter dogs and just dogs in general. These are generally dogs that are under-exercised, hardly have any training on them, that sit in kennels 8+ hrs. a day. Vast majority of those dogs don't go out and bite people, or act aggressively.
Sounds like this dog is at least getting SOME kind of exercise, yet still made a point to somehow get free of its leash and get out of the yard (which should've never happened, so owners fault there) and bit a kid, causing her to have to go to the hospital (so this doesn't sound like it was a "OMG you're weird let me give you a warning nip" type of bite). Of course none of know exactly WHAT happened, but I can tell you that if any of MY dogs went out and did that, they'd be put down. OP also mentions that the dog is "aggressive to any kind of people".. that is just NOT the type of Pit Bull we need out there in the world. Of course, I'm also someone who doesn't tolerate HA at all. I would never own a dog that bit someone.
Sure, I guess if the OP is willing to really work with the dog, and perhaps keep it behind closed doors when there are kids and other people around, then whatever, keep the dog. But if the dog is unstable as it seems based on the OP's posted, then yes, putting it down should be considered, IMO.