Football is deceptive. To make it onto the field you have to be able to pass an Intellectual skill test as well as the Physical skill tests. To improve your Intellectual skill, go to the second floor in the Library & browse the bookshelves. I recommend getting your Intellectual skill up to at least 3.
As a possible 'in game' option, having the Football coach throw a playbook at the PC after they fail the Intellectual test, reading the Playbook counts as an Intellectual test & then they have to take it back to the Library where the librarian shows them where they can find others (i.e. browsing the bookshelves upstairs). On that note, we're in an oversexed University & we have yet to encounter a sexy librarian?! WTF?! just kidding, although thinking about it, that would be an amusing location/NPC for Dominance or Submission training (if you know, you know...)