They pick on each other because it's permitted. I couldn't believe how mean the kids were to each other when my son started kindergarten in a public school. Kids were calling each other stupid and babies and all sorts of other hurtful things.
He now goes to a small private school where the word "stupid" isn't even allowed. They're taught to respect and be kind to each other. Picking on and fighting play is not permitted, and I think that's fantastic.
It's not "kids being kids". It's brats being brats because their parents and teachers are letting them be brats. If you expect them to be kind and respectful, they will.
It's not ok to use words that hurt.