Mihawk has literally never been frame as career minded. Most of what we know about him suggests that behind his airs of sophistication there's simply a battle nutjob that would take zero issue throwing his live away in in a deathmatch whose sole justification is testing his swordsmanship.When your young and stubborn, you can feel the world owes you something.
With age comes wisedom.

But who know, maybe Gary liked younger woman? (Of course he does, why he wouldn't be?)