I am not against threesomes with another woman, I am against you having a relationship with another man. Even if I say yes, I will cease to take our relationship seriously anymore, take the pass to bang other chicks (and lie about our open relationship to them) and then eventually leave you when I no longer care.
That was stupid of you. What you should have said was "I'm cool with it as long as you are cool with me fucking other women. If you don't wanna be in a real relationship we can just mess around and you'll do you and I'll do me."
That way you have the power to walk away without her being able to rationalize a way in which you're guilty and blame you for it. Also it leaves the door open for still being able to fuck her which is always a plus.
What you did was give her the power in the relationship to decide how things will proceed with you. Now she'll blame you and still fuck other guys at the same time and try to paint you as the bad guy and will probably even shut down the potential for maintaining a friends with benefits scenario in the future.
So, leave basically?
Yes by setting the stage that you know it's over but you're still willing to entertain the idea of fucking her even if you aren't in a relationship that puts the pressure on her to want to try and keep you instead of the other way around where you're trying to convince her to stay. ---