The BOM Ambassadors say

Emotions aren't really right or wrong because you can't feel in a right or wrong way, your feelings just are what they are and what matters is handling them in a healthy, respectful and constructive way. It seems like your boyfriend is viewing this as an issue of trust, not respect, and so he's focusing on trying to help you see that you can trust him and that he will be faithful to you even if another girl is paying him a lot of attention. If the problem is that you feel disrespected by this girl's behavior, but you don't feel insecure or worried about him cheating on you with her, you might want to let him know that you trust him and you're not concerned about him cheating on you but you have a problem with her flirting and the fact that he allows her to act flirtatious towards him bothers you, even though he doesn't act that way towards her. It's important to be clear about how you feel, while being respectful of your significant other. You could let him know that if he doesn't feel comfortable talking to her about what you feel is inappropriate behavior, then you are going to respectfully let her know that you feel disrespected by the way she is "Facebook flirting" with your boyfriend and you would appreciate it if she could be more respectful of both you and the relationship. However, if this is affecting your ability to trust your boyfriend, it could be really important to let him know how you're feeling so the two of you can talk about it and hopefully work through it.