I'm going to be real for just a moment.
I think that if he doesn't somebody soon, he'll end up dying and Hunter x Hunter will be incomplete forever.
It wouldn't be the first manga to go unfinished after the mangaka passed.
It makes sense. 13 episodes is the typical cycle for a season in an anime series. But it's still season 1, so I guess they wanted to change the outro for the 14th episode. For some reason....