This is all a bit silly.
We don't know enough about the people concerned to know if it is merely a self-esteem thing, and excuse, or something more genuine. It could well be the former.
However, please consider that he could be being very genuine, decent and open. Some people simply don't have a problem being in open relationships, and that's OK. Others might not understand, but everyone has different ways of relating to sex and relationships. Blanket statements like 'all guys want this', 'most girls will never accept it' etc etc, are flat out incorrect.
I've been in a relationship for four years, and when we both go to university this autumn, we have mutual permission to sleep with other people. So long as we are self aware and communicate properly, I'm sure we'll be fine. I don't even know if it's something I'm going to pursue - I'm very happy with my relationship - but seeing as we are both young, and also want to stay together, it seems like the best way to deal with the situation. Some people might not understand that, but I'm talking to the OP - there are guys out there who would say something like that for honest, genuine reasons. I don't know if your boyfriend is one of them, because I don't know him, but you do and you have to make that judgement call.
So OP - talk to your boyfriend. Maybe re-evaluate the way your relationship works. Relationships change as people change and learn more about each other, and that's fine. I know it sounds a bit silly, but try making a
Want/Will/Won't list for your whole relationship. It's a good way to work out what you both want and you can use it for pretty much anything. However, if you think it does come from a deep seated self-esteem issue, do not take him up on the offer. You will have to do more work on the relationship or give it up if the problems are too great.
Good luck