As arguably Priam should have given Paris and Helen (who after all endangered their people for their personal pleasure) to the Greeks with his thanks, thus saving a whole lot of trouble, one could say that The Iliad is an example of this.
Where King Arthur chooses not to change the law about burning adulterous wives after Guinevere's affair with Lancelot is revealed. He is not (particularly) jealous of them. He loves Guinevere, he loves Lancelot, he is the king and the law is barbarous, but no, he will not change it, he will keep it for some vague noble reason which is never sufficiently explained.
In all the King Arthur stories, Arthur is just Lawful Stupid. Now there is a good reason why he doesn't just ignore the law, because he is trying to get this new concept of "Rule of Law" to be adopted. But Honor Before Reason is at work here, as he could just pardon Guinevere and Lancelot, as he is the king. And should he actually use some compassion, he could then get the law amended so future cases of adultery don't involve the death penalty.
The death penalty isn't for adultery - it's for treason, which both Lancelot and Guinevere have committed by betraying the King's trust. Whatever his personal feelings, he can't afford to change the law, for fear of giving other, more serious traitors a loophole.
It's also been theorised that Arthur actually thought this through, and arranged for Guinevere's public execution on the assumption that Lancelot would rescue her - resulting in the two of them alive, together and out of his jurisdiction. It almost worked, as well.
All of the above are modern interpretations of Arthur's behavior. In the old Romances he is seriously pissed and more than happy that his wife and her lover should die. One can scarcely blame him. Not only have they humiliated him before the entire kingdom but he has consistently defended them from accusations that are now proved true.
The Ăsir not killing Fenrisulfr and J÷rmungandr when they were small. Then again, the Norse did love their inevitable doom as thematic material...
In a strange way, also what they actually DID do to them. Just because a prophecy said so, they kidnapped and imprisoned some weird but currently harmless magical animals, causing them to actually have a reason to want to kill the gods when they inevitably escaped.
Weird variant with Loki, not particularly known for his sense of honor, who in two different myths is caught and coerced by a giant (Thiazi in one, Geirrod in the other) into promising to lure someone into a trap (Idunn and Thor, respectively). Afterward he goes ahead with it even when he's out of actual danger and it's sure to get the other Ăsir angry with him. Myths Retold speculated that Geirrod had compromising pictures.
This is pretty much the best way to defeat a kappa (a Japanese water imp that resembles a monkey with webbed hands and feet): the source of the kappa's strength is the water-filled depression on its head. Bowing to a kappa will make him bow back, and cause the water to run out, rendering him helpless.
A lot of Japanese monsters are like this. There's a particular woman ghost with a slit face who will approach you and ask you if she is pretty. Answering honestly will make her kill you out of anger. Lying about it will also make her kill you. However, one way to escape is by saying that you are terribly sorry, but you have an appointment that you must keep and do not have time to talk. She will apologize for holding you up and let you go.
More folklore than mythology, but supposedly Dick Turpin took advantage of this in his victims by forcing them to swear not to turn him in or testify against him, which they actually stood by.
This is basically how The Devil ends up defeated by mere mortals in many tales, especially in American folklore; he's the source of all evil, a conniving trickster and lies easier than he breathes, but if he makes a deal then he will follow it to the letter, even if he has the metaphysical power to just yank your soul out on principle and laugh all the way back to hell. So long as the deal (or resultant challenge of it) is not worded too ambiguously, anyway.