This is called an unhealthy relationship. Using the threat of leaving a relationship as a bargaining chip, to blackmail people, is emotional abuse. It's far better to be alone than to have a relationship like this, in my opinion.

It certainly can be, particularly when when one partner is dependent on the other for more than physical and emotional rapport (ex. finances, living space, etc.) But a person's willingness to remain in a relationship with someone else certainly depends on that person's behavior. If whether it's worthwhile for a person to remain with a particular partner hinges upon the partner's willingness to enact a certain behavior, is it really never acceptable for the person to offer their partner that information and give them the choice of whether to enact the behavior or have the relationship end?

Sticking with a relationship with which one is unhappy out of refusal to hurt one's partner by leaving is also an unhealthy relationship.