A good girlfriend wouldn't ask あなた to dump your best friend... But on the other hand if she thinks there Using あなた and she is looking out for あなた (as in she has your back) then Listen to her! Your girlfriend should be your best friend anyways and if あなた would pick your friend over your girlfriend then why do あなた even want her in your life? But the decision is really up to! We (on fanpop) don't really know what's going on!!!
Your girlfriend sounds like she's jealous of あなた spending time with your best friend. If your spending too much time with your best friend, spend もっと見る time with your girlfriend so she won't have problems または complain. I think she sounds really jealous, unless is a girl that is your best friend, that's a serious problem.
I think あなた should take it into consideration, but if あなた can't see a real reason, then just be フレンズ with whoever あなた want and your girlfriend can't stop you.