Ok, let's see what arguments Loafer might give to take desired Role.
1. He already knew they would be enrolled today and got ready. This one only Nerd knows, but he can show his preparation items. This prediction surely makes him closer to the Magician.
2. He has Tarot Deck with him, which tell people he knew even about Theme of the Class. It's a Miracle worth of the Magician.
3. His name is literally Solomon. This figure often associated with magic and mystical practices, particularly in folklore and legends. Loafer fits the bill.
4. He is willing to use this power to help his classmates. Use this argument as a possible bribe, who don't want this Role anyway, but wondering if Sol worth supporting.
5. He migh use his knoweledge and ability to ruin a reputation of bullies for a moment, if they try something against him. Or he can move against them anyway just to bribe Athlete and Nerd to be on his side. Make a coalition of sorts to help each other.
6. Could maybe ask for a pity acceptance from other that while he fit the role, he also need it for he has so little will
7. Possible bluff/prediction option: "Hello, mr Educator, I'd like to hand in my first piece of homework now, ahem: King Of Swords, Eight Of Wands, King of Wands, Ace of Wands, Page of Wands". - if it's an assignment like 'using only a series of at most 9 minor arcana, communicate [The Metaphysician Is The Educator's Greatest Student] for example.'
8. Possible rational argument: "Every one of us should get most potent and suitable Role for them, because after we graduate we would come back into the world with other more experienced Enrolled". - I think, what audience believe is true matter more here. It's an argument, where goal is not to find a truth, but make other believe in our position and take it as truth. If they think this Role is really suitable for us, than this second reason may be useful.
9. It is possible to argue as the magician one should be skilled at anything they try. Risky, but maybe.
These are all I could remember from top of my head, came up with or ask from other people.