i think he is the typical trend dieter who will - while strongly commited to the diet lose weight - but at some point her will crash and burn and (a) either get sick due to his very deficient diet or (b0 gain all the weight back, and then some.  having worked with clients like this for many years - it can be really hard to reason with them.  but for the same number of calories his cheese is giving him - he could be eating lean, low sodium turley, beans and legumes, egg whites - all for protein, certainly fruits and veggies in portioned amounts, and some healthy fats like a handful of nuts daily, a small serving of avocado or olive oil.

His nutrient deficits will catch up with him - but I confess, if he is "determined and stubborn: and only willing to eat this way - you may have a tough time getting though to him.  If he does have a relationship with a doctor - or a valued friend - you might appeal to them to help - with the core message being "your concern."