Is it okay to ask my boyfriend to give up his ex-gf as a friend?

My boyfriend and I have been talking since last Nov. and dating since this past January. Things have been amazing but he has a big problem with me being friends/talking to my ex-bf and so he asked me to stop talking to him. My ex-bf and I were really good friends for about 4 years and dated for a 2 weeks before... show more My boyfriend and I have been talking since last Nov. and dating since this past January. Things have been amazing but he has a big problem with me being friends/talking to my ex-bf and so he asked me to stop talking to him. My ex-bf and I were really good friends for about 4 years and dated for a 2 weeks before calling it off because it was just not going to work out. Nevertheless, I love my current bf and I can see myself spending my life with him so I did as he asked and gave up communication with my ex.
He has an ex with a similar friendship background except they dated for 3 years. At first I didn't really care about him keeping in touch with her and whatnot, but lately I have been getting annoyed. She calls him at all hours of the night asking to 'hang out' and they sometimes do lunch. After this, I asked him to discontinue talking to her like I have for him but he argues that "he still cares for her and their friendship." I don't know what to do, he keeps arguing with me!
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