There are actually plenty of adversarial situations in which it's beneficial to give yourself a handicap in order to win. If you're playing "chicken" (where you drive cars at each other and whoever turns away first loses) you can blindfold yourself and remove the steering wheel. If you're doing Mutually Assured Destruction, you can set up an automatic retaliation system which you are unable to pause or cancel. By removing some of your options, you can effectively signal to your opponents so that they are forced to respond to your strategy.
Similarly, it can be beneficial to act "irrationally", because if your opponents are rational actors, they won't even try the strategy against you. E.g. If I know you will "irrationally" come for revenge after the fact even to your own detriment despite the fact that it won't fix anything, I might not try something against you in the first place.