Why are popes always really old?

Technically, they don't have to be. They could elect a venerable whippersnapper cardinal - Dan Brown wrote a book about that. And that tells you how likely that is if he wrote the story. But it is possible.

It would be rare because it takes seniority to get into the position. And politics to be well liked enough to be put forward and then elected. By mostly old people. Some of whom would like the job themselves.