He wants to stay friends with his ex

Ok my boyfriend and I have been dating about six months and just recently I found out he has been talking to his ex. They were together 4 years. We talked about it and he said he loves me and If it made me feel better he would stop. I feel as though it would not be fair, because who am I to say who he can and can't talk to. Also I keep in touch with my ex's (It is not nearly as regular). They speak on almost a daily basis. He broke up with her and I know she still cares... Am I wrong to say he shouldn't talk to her? Why would he even want to keep her so involved in his new life?
He wants to stay friends with his ex
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