You're being asked to imagine yourself as the executive - you're the person with firing authority.
A manager who works for you asks you to fire someone on their team. There are a hundred people on various teams in your group, you don't have first-hand knowledge of all of their performance. You want to have a system in place for making sure this is a fair request, vs "we argued a few times the last week" or, in the really bad sorts of cases, something like "we had an affair and it ended badly and I'm trying to clean up the mess by firing them."