I've certainly experienced that, but I've also seen a fair bit of kindness from very young children as well.

For example, a few years ago, one of my nieces, when she was four, got a bunch of candy for some reason, and desperately tried to give everyone a few pieces. She wasn't asked to share, she just decided that she'd give everyone a bit of candy, and as far as I can tell it was purely just to be nice.

That said, kids are often sociopaths, I was definitely a little shit when I was a kid.