If I pushed someone's baby, should I admit it?
Did you actually do push them, and how does it make you feel?
It makes me want to puke.
I understand why you would feel sick to your stomach if you intentionally pushed a baby. That's a cruel thing to do. You should apologize immediately to the parents and make sure the baby is ok.
That's not how I do things.
If apologizing is not in your nature, then you need to work on that. People are expected to apologize when they do something wrong. It's courteous and shows the other person that you regret what you did.