I definetly don't think you should break up with him. It seems unfair that he would be ok with his one-night stands in the past with random girls, but have such a problem with your friend with benefits. Sometimes I find guys can be really sensitive, so if the topic of past relationships comes up with my boyfriend, I just tell him to let the past stay in the past, that it's not important to our relationship in the here and now. I think it is good to have an honest relationship, but things are private, and you really don't have to share everything with your partner. If there are some things that really wouldn't have an impact on your relationship, or something that he could live with not knowing, then I wouldn't tell him.
Also, you didn't cheapen yourself as he said. If he can have one night stands with girls, which is kind of the equivalent of just using them for sex, why can't you have had the same thing with one guy? I think you should make that clear to him. Double standards aren't cool. Also, I would let him take his break. Don't contact him, you did nothing wrong here. He will come around and will probably feel immature for acting the way he did. He should just accept that no one can change their past, even if they want to, and its no way to live worrying about it.
Good luck