So, not to step on yumapple's toes here, but your school kinda can stop you from doing a subject if they want to. VCAA has no statement on the power of schools to control your VCE, so they have every ability to tell you that you can or can't do something. Is it unfair? Maybe, and I personally experienced that unfairness back when I was in school (my concern was different - I wanted to do a subject by distance, and the school said that they wouldn't let me drop one of the school's subjects to make room for it, effectively blocking me from doing the distance subject), so I can feel your frustration. However, this isn't necessarily a bad thing.
Some schools (particularly higher ranking schools) will make these decisions to protect their own vested interests. If you do food studies and end up doing poorly because you did it a year early, then that would bring their rank down, and look badly on them. It's disconcertingly common for schools to try and gatekeep some subjects so that their ranks are preserved, even if they put students at risk of not meeting uni course pre-reqs. HOWEVER, you should remember that there are a LOT of schools that are out there to protect their students, and I think your school is one of those based on what I'm hearing. If you do food studies early and do badly as a result, it's going to look bad on them - but it could also cost your aggregate points that mean you don't get into the course you want. Based on their wording, that you need a "compelling argument", I think that they're still open to the idea of you doing food studies 3/4 - they just think that you may not have thought things through enough. Maybe you have and you just need to prove to them that you have, or maybe they're seeing something that you can't - something that comes with experience from watching students accelerate before they were ready, or from the actual food studies teacher who has watched ill-prepared students take the subject and fail before. It sucks that they won't let you do something, but try and see things from their perspective - they're likely just trying to protect you.
Things you can do? The obvious one is give up and compromise - maybe they won't let you start a new 3/4 out of nowhere, so maybe you'll have to take legal studies. Maybe you take food studies 1/2 and have the standard 5 subjects in year 12 like everyone else (you CAN do 4 3/4 subjects and a university enhancement subject, that's okay). The other is you cause up a stink - you argue with the person in charge. Then you argue with their boss, and their boss's boss, and maybe even someone else's boss (the VCE coordinator? The 3/4 food studies teacher? The vice principal? The principal?), until you find out that they won't bend, or they finally give you what you want. But it sounds to me that you really need to prove yourself, so I think it would honestly be worth learning some of the 1/2 study design even right now to prove to them that you're capable and will be able to do the acceleration. Maybe mention how good your other grades are, or note your poor marks in legal studies (making assumptions, I know nothing about your scores).