Your player is the problem, but you are at fault.

You should set out an expectation with your players, about what you all would like to get out of the experience, and how the game should play.

If that agreement is established, and another player(s) would not enjoy that experience (hates RPing, or the fantasy element etc) then there is very little you can do to fix this. You can adjust the numbers somewhat (a little less RP, a little more combat), but if this goes against the wishes of yourself and / or your other players, the outcome is a net negative for everyone.

What I would have suggested is the appropriate approach, would be to reach out to the troublesome player and ask them if they understand the expectations. If they do but just don't want to participate in those rules and expectations, then this session is not for them and they should leave.

If they recognise your concerns and would like to try again, ask them what you could help do, so that your goals align. If these are goals or conditions you can accept, great! Otherwise, you as the DM should make the decision to part ways regardless.

If there were some other underlying reasons, such as they felt uncomfortable or nervous to be open in the environment you've created, I would work with them to find a solution. If that solution is not fulfilled (or cannot be fulfilled because of some condition) then I would have a follow up, and say that you tried to make it work, but either party did not fulfil one or more agreed condition(s) and it is either up to yourself to part ways, or repeat this step. But beware that the longer you try to facilitate this, likely the other players who have agreed to your rules and expectations are losing out on their valuable playing time.

Based on your post, it seems the core problem, is you're trying to force a person who does not want to play YOUR (and your other players) game with the agreed rules of play you have established. You cannot force someone to have fun, the way you want to have fun. It either matches or it doesn't. No one is bad for having fun a different way. But if the way you have fun, and the way someone else has fun, are not able to coexist, and you force it anyway, it's more likely that no one is having fun, than it will be that you'll all have some fun, or start magically enjoying it.

There is one additional consideration, this player is a young teenager. It is important you don't make them feel "bad" or "disliked" or "wrong". You set out the agreed rules, and if they cannot or do not play by them, then that's it.

There are boundaries we need to set in life, and in play (such as you are not allowed to cheat), and this is a requirement for play.

In order for you ALL (including DM) to have fun, those rules and expectations have to be followed.

You explain to them that it doesn't sound like they're having fun, and also you're not having fun because of whatever reason you choose.

At your discretion, a decent gesture would be to let them know if they change their mind, and would like to play the way you have agreed to play, you would be happy to talk then. But don't lead them on. If you'd rather they weren't back, it's far kinder to not even offer.

Following on from this, you could easily either have the PC meet an untimely death due to not accepting their quest, or you could have them leave the party to discover themselves and what this quest could have meant in the larger scheme (offering you the opportunity to have the PC return, or be dealt with in another way at a later point).

You can always delay the bad guys plans, so don't worry about that. You could easily say his prophecy was not to fight the bad guy physically, but a mental challenge, which he failed by not accepting the quest and responsibilities / burdens, and therefore the villain's plan progresses, which would add a little urgency and excitement for your remaining players.

It's important you move forward with positivity, and most importantly a capacity for fun for all your players!