Why is it a fight for my boyfriend to stop talking to an ex?

alright so heres what is going on. This girl has caused alot of problems between my boyfriend and I. I know its only facebook but i have noticed everything he posts on there shes commenting on and liking and being flirty with it. She does have a boyfriend. My boyfriend and I are expecting a baby in June, and everytime I tell him it bugs me that she is even talking to him since she caused alot of problems, like us breaking up the first time he gets mad at me. He refuses to delete her off facebook and says he will just delete his account. It is to the point where im fed up because I gave up alot for him and all i asked him was why she is even on there and told him i do not care for her. Wouldnt it be more important to be with your girlfriend and baby then talk to an ex, who causes problems? I also have noticed when i tried to put im in a relationship with him he wont accept it and he never says im his girlfriend, just a girl that hes having a baby with. Should I just end it because I dont need this and I do not want my other kids around this crap. once again i know its just facebook and i wouldnt care if it was not affecting our relationship