We've all come in contact with the "bow out" before. The fake humble move where someone pretends to be above a "petty" argument or disagreement just because they want to look like they have the upper hand, when in reality, it's because they're afraid they'll be found out.
No one wants to be humiliated. No one wants to be called out or proven incompetent, which is a huge reason why people "bow out" of something they can't do and act like they're above it all. The problem is though, at the end of the day, we're animals. We can smell when someone is full of crap, whether we realize it or not. And all of the intellectualizing, defending, and rationalizing won't really convince anybody you're being honest.
And when it comes to "bowing out" there's no better example than dudes who pretend to be "over" women who want nothing to do with them. Just take two seconds to look at any girl's messages on any dating app and you'll see what I'm talking about. But there are some men who take the whole bowing out idea to the next level.