The feelings of a violated and betrayed spouse should be a LOT more important than his need to socialize with women in private.
If he can't GET THAT.. Then you have a SERIOUS red light there on his ability to meet your needs long term in this marriage... He is wiling to make compromises that are to your disadvantage here... HUGE RED LIGHT about his ability to be a man and a husband.
Even if he gives in at this point I am worried. He clearly doens't GET IT.