I Need to Leave, I Can't Be in This Relationship With This Other Person

No one is entitled to be in a relationship with you, not the incoming partner and not the established partner. You get to decide about what's best for you and your life. It's really not cool to push someone out or say that someone doesn't work for you just because you don't want to be uncomfortable. If you're trying to use setting boundaries as a way of trying to control them then that's not okay.