I think this question is terribly opinion-based. At least my answer is.
First of all, it might be very difficult to motivate a 12-year old! She might be opposing the idea just because she wants to oppose things and/or people. Maybe if she saw someone that she looks up to, someone who fluently uses the concepts of tonality to do something that's cool and ossom, she might get interested. Music theory is not very cool! No street credibility is on offer on those lessons. No immediate gratification either - unless you like to tinker with meaningless puzzles.
How do you influence and motivate people? Bribery, extortion, ... and what have you. ;) But that sort of extrinsic motivation isn't very good. I've heard that intrinsic motivation is the most effective kind: challenge, excitement, enjoyment, fun, fascination. And if the person already has a potential for intrinsic motivation, adding extrinsic motivation might actually counteract the positive things! If she happened to enjoy music theory, if you say that she must do it to be a good girl or otherwise there's a punishment or something, or if there's a reward which makes it more like a chore, chances are that she stops enjoying it! But there's one more type, provocation, which might be able to turn into intrinsic motivation ... I'm not sure. Ask a psychologist or something. :)
Make it enjoyable
IMO, the most effective ways to get someone to start learning is to: (1) make it feel possible by providing them simple, doable examples that they succeed in, (2) show a good example person to look up to, and (3) to offer a time, place and means to practice the thing and excel in it.
How do you do this with music theory, if it's taught theory-first? I have no idea! IMO it has to be practice first. The things, in this case concepts of tonality, have to have an immediate practical use that feels good. And that is: playing songs by ear! (And then, making modifications to them by ear - though I'm not sure if everyone enjoys that sort of messing around with songs which are almost sacred things. Many people have a weird preconception that songs should be played correctly, which is, exactly like it's on the famous recording everyone knows.)
For example, why I learned tonality as a kid - I loved to play songs by ear, as chords and melody. It felt much better than listening to radio or something. A good song was even better if I could play it myself. First it was 3-4 chord songs in simple keys like C/Am, F/Dm and G/Em. Then it got more and more complicated and I expanded to all keys one by one. Add borrowed chords, modulations, modes, altered chords, ambiguous harmony like dim7 chords, tritone substitutions ... for most of that stuff I didn't even know the proper names. Like "dorian mode" - it felt weird that there was such a pompous fancy name for such a simple thing. There was always some song that had a trick I didn't know yet, so there was (and is) no maximum level to achieve. I also had a place and practical situations to actually perform, in school, in church, at home, family get-togethers ... accompanying songs and playing small solos. Every time I played anything, I imagined an audience or band or other "real" situation together with other people. I knew it was pop and not fancy classical music, but I didn't care, it all just somehow felt like the right and proper thing to do. And I think it hasn't changed, I think nobody opposes singing songs?
Provocation (probably a bad idea)
This is probably a bad idea, but just to explain the idea through a "warning example":
If you don't understand tonality at all, what kind of a musician are you? A robot that cannot play even a single note without someone else writing the note for you. In my very subjective opinion, being mentally tied and handicapped like that is simply pathetic. An "artist" who cannot express herself. Ok, if your thing is to spend your musical life repeating what is written for you and do exactly as you're told, then ... "fine". Though I don't think that's really fine at all. Wouldn't it be kind of nice to even know a little bit of how the things work? Isn't there something wrong, if you don't know what you're doing, if you don't understand the sentences you're being told to repeat?
Maybe that's too negative. It probably won't help saying things like that, unless you can provide a readily available way to try something better. Probably not even then. You don't have to motivate a dog to give up the bone he's chewing, if you give him a steak instead. (Imaginary example, I know nothing about dogs)
Remember that trying to add extrinsic motivation may have the exact opposite effect of what it tries to achieve. If the student isn't shown, if she doesn't experience first-hand, in practice, how the concepts of tonality are used to achieve something "cool", in a way that she can replicate, then there's not much you can do. (And I also think that if the concepts are taught top-down, theory-first, to people who don't practice playing songs by ear, then it's taught wrong.)