confused and in doubt

My girlfriend and I had a mini-breakup, and we both said unpleasant words. We’ve been together for almost a year, and to say that the relationship is turbulent is to say nothing. It’s like a roller coaster every week. I don’t know if I like it or not. We’ve quarreled before, and we’ve always passionately reunited, so I’m used to these moments. But I can’t get it out of my head that this last time she told me I can go and have sex with anyone I want, she doesn’t care. Nor did she care before. How can a person be in love with you and be indifferent to you having other partners? When I ask her if she’d cheat on me too, she always says she wouldn’t. Can a woman be so weirdly non-jealous? Or is something seriously wrong with our relationship?

Thanks for listening. I’m in half-mind to break up for real.