What should i do if my boyfriend flirts with another girl?

[Soso]

We have been dating for 3 months. He has had not added me on Facebook and I haven't even asked him about it cuz I don't really use it that much.......Sometimes when I check him on Facebook, I see that he comments on some posts that girl and his comments are obviously flirty! ( I check him to just make sure that if hes sincere with me and also to be honest, I just wanna a proof that can make me stop being insecure) Yesterday, I was in his house and I asked him to open his Facebook and he did, so I started looking on who message him and who contacts him and then I asked him for his password and he refused to give it to me!! I was really upset when he refused and it actually made me feel more insecure!!!! He is really affectionate to me and I know that he loves me and I love him too but I just don't know why he doesn't give it to me. I also really respect his privacy but because one time I saw that he flirted with that girl so I started being paranoid. I just don't know how to talk to him through it cuz it really bothers me when he flirts with other girls.