I've basically had the same type of relationship as you for the last 4 years(4 years this August), we've been on & off the whole time, together probably 2 1/2 of those years(were together right now), personally when we were off I couldn't be friends with her, I would never had been able to see her with another guy, or heard her talk about another guy. We're really good friends when were together, she was & is my best friend, but seeing her with someone else would be to much to handle, maybe she feels the same way with you, that she just couldn't see you with another person, or she doesn't want to put you in that situation of you seeing her with another guy.
Woman do love to play head games with guys though, it's like a sport to them.