Car accident

So I hit a parked car that was in a no parking zone by reversing. We got each other’s insurance, took pics. My car is fine and his has a little dent. I have a smart car that usually beeps so why it didn’t beeping alert me today? Idk. He doesn’t want to go through his insurance since he just got a claim on it. He wants to take it to a shop and have me pay for the damage (understandable). But should I pay through my insurance or pay out of pocket without insurance? What would y’all do ? Do you think it’ll cost a fortune for this dent ? It was my back left bumper that tapped his car. This is also my first accident.