Breaking up hurts, but being "strung along" is worse. I myself have advised coming clean due to the ever-more extreme pain resulting from the inevitable breakup. In the end, your ex-partner will be better off when they get over you.

Is this obviously true? Note the underlying assumption that you would break up eventually. Suppose you're dating someone, and the relationship gives you 1 hedon and them 3 hedons. You discover you have another option that gives you 2 hedons, but their next best opportunity gives them 1 hedon. (Suppose, to make things easy, those two other options are involved in a relationship themselves, which gives each of them 1 hedon.)

If you just sum hedons, you should stay with your current partner. But that doesn't maximize your hedons, and the locally optimal move is to break up and date the other option.

Another consideration: suppose you're dating someone with suicidal tendencies, and you know that a major immediate cause of suicide attempts is the end of a relationship, but you were unaware of their suicidal tendencies when you started dating. You're pretty sure that you will be less happy in this relationship than other options you have, but think that they will pose a serious risk to themselves if you break up with them. To what degree can they manufacture an obligation for you to provide emotional support to them?

Management is an unsolved problem in society, but the co-workers of that employee will almost certainly conclude that he did not deserve to be fired.

Both of these strike me as contentious. Few people are satisfied when their coworkers are incompetent or slack off, and we know quite a bit about effective management.

Perhaps his happiness is outweighed by the distributed quality of the company's income and the remaining employees? Management often does not make its reasoning entirely clear.

Certainly there must be cases where the option that maximizes profit does not maximize happiness, unless happiness is defined as profit.

Stealing someone else's partner is considered to be a very bad practice. It is also existentially risky.

But this ignores actually doing the math! Suppose it is known that she would prefer abcd_z's company to the other fellow's, and abcd_z would prefer her company to no one's, and the other fellow would prefer her company to no one's, but his preference is smaller than theirs. The "stealing other people's partners is bad" is putting precedence above greatest good.* The claim that it's existentially risky is one that doesn't require utilitarianism; a selfish person is more concerned about those sorts of incentives than a utilitarian.

*"But wait!" you cry. "There are second order effects!" Yes, but it's not at all obvious that they point in the direction of not competing for attention. Consider a club where this injunction is taken seriously, and applied very early- basically, a woman is obligated to go home with either the first man she shows positive attention or with no one. Then this dramatically raises the bar for flirting, since she needs to be fairly confident the guy she's interacting with is her best option, but she needs to make that decision at first sight! In a situation where it's alright to compete at all stages of the process, then moving forward with one person has less opportunity cost, leading to more efficient pairings and means of discovering them.