Going to have to agree with MLO4H; you are quite naive.
Think what you will, but I'll stand by my statement. Creating a facade of compassion for someone you ultimately desire to end your relationship with only generates misunderstandings, lingering attachment & disappointment. In general, this "compassion" is not something someone does for the benefit of the person being let go, but is a selfish desire to relieve the guilt of the rejecting party. It's far better to cut things off clean. It's far more thoughtful to the rejected party.
How is it at all unstable to not be able to switch your emotions on and off like some kind of robot? That's not unstable, that's human.
For most of us, self-preservation is a dominant instinct. If someone attacks you or, for example, wishes you dead, for myself, I make an immediate break with that person emotionally, and in my experience, many do the same. Anyone who doesn't is bound for serious suffering. My condolences to those who can't.