There needs to be an underlying appreciation and love of playing music. They have to feel that they are free to explore music by themselves.
Perhaps, but from the description in post #1 it seems he thought his playing was bad by himself. Which at least suggests he appreciates music enough to care, get frustrated and lose his temper over his own playing.
Sometimes people practise for too long [a good example was the girl in the Classical Star programme who was in tears] and they just need a break, not someone telling them "try this" - if his playing is genuinely good [and hers was] and, more importantly, getting better despite his frustration, this may well be it. Just have a break and try tomorrow, or in a few hours.
Had he lost his temper because someone else thought his playing wasn't good enough then I'd see your point.
I know my own experience is similar, I hate playing - I feel physically sick just thinking about playing the piano. I do it because it's a compulsion. An obsession. If I were 10 I've no doubt I'd be in tears, and smashing the piano up. It takes an awful lot of self-control not to do that as an adult. Playing the piano, if you're one of these people that can and doesn't realise what it feels like not to be able to do it is immensely frustrating. Worse, if you're ten and someone decides you don't have a love of music, might be dumb, or are lazy, because you are frustrated at not being able to play and quite possibly cannot correlate the advice /teaching you are being given and how to apply it.
Imagine asking me for directions to somewhere you desperately want to go to, and, no matter how much you misunderstand the directions, no matter how many different people tell you, no matter how they are confident that they know how to get you there despite your tale that you've tried for years, you've been wandering around and around again and again, and are still lost, listening to other people that are there. Think of the most frustrating day you've ever had and imagine having it every day for years each time you sit at the piano. Or think of each time you've hear a piece of piano music, in an advert, on the radio and you've been motivated to play that piece. Imagine instead that every piece you hear reminds you of the fact you can't play that piece and have no idea how you ever will.
"freely exploring music by myself" is precisely what has caused pain, frustration and anything but a love of playing.
Perhaps he'd love to play if he could see a path, however long, that would lead to improved playing. At best the lad is wrong about his playing, and if he does what he is already doing that improvement will happen. At worst he'll just have asinine advice like "practise" or "use arm weight" "pronate your elbows" "imagine a beautiful tone and it'll happen" "play hanon' "no don't" "yes do" "no...it'll lead to injury" that means nothing.
At the least he needs to make progress. He needs someone to teach him in way that allows him to perceive that progress.
At that point if he doesn't care and / or isn't happy playing I think you're spot on, but from the post it could just as well be someone who really wants to be able to play but can't - and he's potentially in for a world of pain there if my experience is anything to go by. Much better to not give a crap about your playing until you discover you can play - because a love of music isn't a benefit if you can't play, it's a curse.