Should I let him move on?

All relationships, even non romantic ones, come to a point or several points where a little break is healthy. Just give him his space for a while. Letting him go or not is not your decision its his, so just give him some thinking time.

Let him go if he wants to. Not that you have that much of a choice, but clinging more seems counterproductive. Have you actually been acting different lately, do you think? Does he have a genuine reason to mistrust- I mean, you didn't cheat on him. You kissed someone when you were broken up, did he expect you to stay "true" to him while broken up? Kind of ridiculous. Maybe he has been hurt in the past. Whatever the case is, let him be.