My gf wants me to be friends with Girls... don't get it wrong here but ......

Such behaviour displays certain amount of insecurities in her part and some kind of defense mechanism. She seemingly want to play games and you seem to be always at the losser end. If you are serious to her and don't want to "eat" her bait then you can tell her that games belong to play grounds and not in relationships.

I don't know why but so many women are insecure in their relationships :( It seems that your girlfriend is testing your loyalty and faithfulness by pushing you to have female friends. It's unfair to say she wants you to have female friends and then to accuse you of suspicious behavior with them. That is just playing mind games with you. I would be upset if I was in a relationship where someone did that to me. Perhaps you need to have a serious conversation with her where you discuss trust and respect and how important they are to the success of a relationship. She might need to be reminded that you are capable of choosing your own friends... male or female... and that she should not feel the need to do this for you.