My boyfriend is asking for permission to cheat? why?

Since he is brave enough to say it like this give him the following decision.

Slap him first with a smile on your face.

Tell him he have 2 options leave you and do what he want or stay and not look outside. That one with a serious face.

Lol “ me or fun”.  Maybe this is why he is cheating on you .. anyway drop this guy he seems like a dirtbag anyway.

Tell him to F off, and get lost, go find a good man. he is not a good man.

If he was only a boyfriend, no I would not stay with him. I would end the relationship immediately. If he was my husband, that would be a different story... some people put a lot of money, time and effort into the marriage and they don't want to throw it all away. Plus divorce is expensive. I think some people feel pressured to stay married.

Poor you - you are clearly more serious about your relationship than he is, as often happens. Guys can take a very long time to grow up, and you deserve someone a little less shallow.

We fall madly in love, don’t we, thinking (feeling rather) that it will last forever and is enough for a serious relationship. However, it’s very hard to live on an emotional high for very long. Eventually we start to come down from the ecstasy, excitement, strong passions and desires, typically after around 18 months to three years (people vary of course). If couples are friends, discuss their mutual values, shared ambitions, interests, etc., in some depth (obviously there will be some differences, which help make relationships interesting), and make plans, work on their personal development, etc., this can develop into a long and wonderful relationship. If one party feels insecure or low in self respect, it can make for a difficult partnership. It's easy to behave at our best when in love, but marriage, for example, requires a lot of self discipline, sacrifice, compromise and flexibility. If a strong friendship is not in place, the relationship will probably peter out eventually - or worse. Quite often we fall in love because we are lonely and allow ourselves to be won over by anyone who takes an interest in us. Thus we give away control to somebody else if we are not careful. This is another reason for taking things very slowly, and really getting to know someone before committing ourselves or getting too emotionally or sexually involved. Sex can be emotionally bonding, which is disastrous if the other things are not there: strong friendship, similar values and standards, common interests, etc. 

Good Luck! I'm sure you'll be with someone one day who will be better for you, and you'll be grateful that this one didn't work out. 

you should dump him now.  no one does this, except cheaters.

It's because you picked an asshole. He's not serious or he wouldn't have that in mind. Dump the chump. Learn from it and move on.