In Logan's Run, they set the age at 21 years old for state
  assisted required-voluntary suicide, which is, in fact, murder,
  but we don't like that word.
  When they made the movie, they switched it to 30 years old.
  Probably all the child actors would have made it awkward to put
  on screen like the book.

  I don't remember the reasons why they chose 21 years old, as I
  never read the book *or* saw the movie, but 21 years old is as
  logical as any other age to pick. It's likely for the same
  reasons we give today. "money" / "resources" / "Young > Old" and
  other strange ideas.