Most insurance plans only cover a maximum of $1000 or $1500 for braces. That's the same amount, by the way, that insurance covered 30 years ago, when braces cost around $1800 in full. Now, it's considerably more.
Yes, most orthodontists will work out a payment plan. If they estimate that you're going to wear the braces for 1 year, then they'll probably only set up a payment plan for 1 year. And that's because once the braces come off, a lot of parents won't bring their kids back for the retainers and other follow-up treatment that you need for the next couple of years, and since they're not walking in the door every month they quit writing the checks.
Are there orthodontists who will stretch the payment plans out longer? Probably, but it's up to your parents to find them. They can also talk to their bank, their credit union, their credit cards. There are options open, but please remember that your parents know what financial obligations they can reasonably take on. If your braces are going to cost $6000 and they have to be paid for in 12 months, that's $500 per month. Your parents have to pay it back, which makes them the only ones who get to determine whether or not it's realistic for them to agree to the debt. After all, you're 15 - you're probably asking for a car, and you've got college coming up, and your last couple of years of high school tend to get expensive.
Our daughter wore braces for a year in junior high. They cost us something around $3400, and our orthodontist stretched our payment plan to 27 months instead of 12. And when I look at my daughter's wedding pictures, with that beautiful smile, every penny was worth it.
But do remember this - orthodontists treat a lot of adults now. They have braces that go on the back of your teeth and they have other appliances for adults that are invisible or nearly so. While it doesn't feel fair that your parents won't pay for braces now, you can still have your teeth straightened later. And since you already know you need it, you can be sure that you get a dental plan that include orthodontia.