Sorry to hear that you are exposed to such a rough situation. I know that I would be extremely disappointed and kind of outraged if my partner would disregard me in this way. As I see it, you told him what was going on, you never did something behind his back and he isn't able to gauge his reaction about what is going on. All fine and well, it's totally natural to be overwhelmed by one's own emotional reaction, but the way he is pressuring you and giving you ultimatums and such ... real deal breaker for me. I would never allow anyone to treat me like this or demand that I should treat another person like this ( in your case the girl you are involved with).
Just for a better understanding: Is this some kind of normal behaviour from your point of view? Who is the one getting his needs met primarily in your relationship? It sounds like he comes from either a place of security, feeling absolutely right in demanding this of you or if he is totally insecure and overreacting in this situation. I can't tell what it is right now. Depending on the circumstances, you should either put your foot down and stand up for yourself or reassure him that he still holds importance to you and you aren't just walking over his needs.
Those would be my first impressions. Of course, I can be way off here. Wishing you luck nevertheless how the situation may work out.
Facts: 30, female, bi, v-type relationship with Sward (husband, straight, mono) and Lin (boyfriend, straight, mono), poly-fi and co-primary.