I think the big issue here is that he didn't tell you beforehand and then tried to obscure later. And it's perfectly fine to feel a bit betrayed.
I've been with my partner just short of a decade now and we used to live in a city with a lot of "gentlemen's clubs." And he had a single friend who always wanted to go to those clubs. He didn't ask my permission, but he did tell me ahead of time, ask if I wanted to join him, and when I said "okay, but remember who you come home to," I know he respected that. And the deal is if I want to go out with girlfriends and see male strippers he's fine with it as long as I also remember who I'm coming home to."
I was honestly surprised myself that I was actually totally fine with him going to a gentlemen's club, but the difference between my situation and yours is that my partner was completely frank and let me impose "rules" on him. Your man got caught up and realized after the fact that it might hurt you and that made it worse.