Yes. You are morally obliged to weigh your desires against the anticipated effects of your actions. However, this isn't usually (for me) a matter of favoring other people over myself, it's more favoring long-term me over short-term me. I want to live in a better world, and that means taking actions that improve it.

Breaking up with someone gently and firmly now is far better than breaking up horribly after years of misery. For both parties, and for both of your future partners. Easy win.

Likewise terminating an employee who's not working out (when that's not likely to change) - it's a long-term win for you, their coworkers (even if they don't know it), and sometimes for the former employee.