You are not going to convince them it's fine as it is and not a big deal. Teen aged male hair length has been a contentious issues since the 1950's when college prep high school guys and college guys adopted crew cuts, flat top crew cuts and ivy leagues and industrial arts greasers and dropouts wore long greasy pomps and DA styles in the wake of a juvenile delinquency hysteria that included televised congressional hearings. This segued into the mid 60's when a lot of the college prep kids wanted to start wearing Beatles cuts and then long hippy hair, and long hair became a symbol of protest to the establishment and draft and war. By the mid 70's almost everyone was wearing long hair but this didn't last long. By the early 80's short styles were back in vogue among the college crowd, with a partial grunge diversion in the early 90's. Even the flat top crew cut had a revival in the mid 1980's that lasted till around the turn of the milennium. If your parents came of age at certain points of time and in a certain area, they probably have deep set beliefs about long hair on teenaged boys that you will not change.
I suggest instead to figure out your head shape, face shape, frontal hairline, neck shape, facial features and type of hair and then experiment with short styles this summer:
http://img34.picoodle.com/img/img34/3/1/7/f_TrustyFaceSm_fcf3e2c.jpg
There are short styles that are just as and probably far more complementary than your present long style, unless you have something like extraordinary ears that are best covered by hair, and if this were the case I doubt your parents would be insisting on a haircut. I'd get a cut that is much shorter than they are insisting on. This kind of strips them of this power they have over you with regard to hair length, and they will realize that you are now in control because it doesn't matter to you. Not being able to drive is a big deal because of not getting a haircut, especially when every other guy is basically buzzing his hair off without giving it a second thought. In addition it is highly unlikely that the most complementary style will be one that goes to the maximum length they are willing to allow. One other point worth mentioning is that it is not only your parents but most adults who don't like seeing long hair on teen aged boys, even those dads who wore it themselves. To some it is a powerful symbol of much that they think is wrong in this country at the present time, while a cleancut young man is a symbol of much that is right and of better times in the past and a better future. Long hair makes a negative first impression on certain adults who a young man may not have a chance to make a positive second impression on, like the guy conducting an interview for a job or college, or the cop who could issue a verbal warning or a costly ticket. Asking you to get a short haircut is almost nothing that your parents are requesting in the whole scheme of things, but it obviously means a lot to them, and is actually to your benefit. Even most potential girlfriends prefer super cleancut guys because it causes their dads to trust the guy and not ask a lot of questions.
You can turn this around and make it a win win situation by happily complying and getting a haircut, and thereby earn all kinds of brownie points. Ask to get it cut more often and shorter than they require and in time they probably will no longer insist on haircuts. You will need insurance, a car and college can be very expensive for students whose parents make too much to qualify for financial aid, so there is an enduring dependent relationship, which your parents are not obligated to support past the age of 18. You can probably whine and make life miserable till they give in but your relationship will suffer and in the end you will get a short haircut anyway. Just take a trip to any college campus and see how few guys wear hair that covers any part of their ear or note how many more seniors wear short hair than freshmen or sophomores at your high school. And truthfully almost every mop haired guy would be more complemented in a regular tapercut:
http://img213.imageshack.us/img213/5761/tapercutlayerontopsidepto7.jpg
http://img138.imageshack.us/img138/5784/fawesomenapem545c8f9ux8.jpg
an ivy league:
http://img266.imageshack.us/img266/2631/kidwithacokezerocrewcutdw5.jpg
http://img301.imageshack.us/img301/4844/fcrewcutarmymc68a9aeic7.jpg
or crew cut:
http://tbn0.google.com/hosted/images/c?q=fb2612a8009c3631_large
http://img108.imageshack.us/img108/8239/chaucersfavelargerwp8ca5.jpg
http://tbn0.google.com/hosted/images/c?q=5fc8a32674f60b33_large
See this answer for an explanation of the classic short styles. Be sure to open the first two links contained therein:
https://answersrip.com/question/index?qid=20090521173336AA1hONk
If decide to get a short cut, take a few photos to help describe it to the barber or stylist.
Good Luck!