Did we ever work out what factors enable a player to be a tutor?

Is it age, squad status, reputation, CA, time at the team?

I can't seem to work out a pattern - I'm trying to tutor a couple of young strikers but I have no options available to me, despite having 3 strikers in the first team who are all set as first-team or key players.

Is there a simple formula for this?

A player who considers his squad status to be backup, hot prospect or young player can be tutored by another player.

Players can only tutor players who play in similar positions (e.g Michael Owen couldn't tutor a defender).

So, in your situation, none of those strikers will consider themselves to be more than backup, so they won't be able to tutor.

This is quite confusing, but thats how it works

The two young strikers are 'hot prospects'. The three senior strikers in my first team (who I want to act as tutors) are first-team/key players. But when I click on interaction options for the hot prospects, they have no tutoring options.

Most likely because the players who you see as first team/key players don't see themselves as more than backup, so can't tutor. Tutoring isn't to do with their contract status, it's to do with their personal opinion.