As long as it's not all hills 22 mi round trip isn't too bad. Mine ranges from 7 to 20 mi round trip with some hills.

I also grew up in a fairly trad Asian family. Except my mum was very supportive of me and my brother's biking. In fact she taught me to ride, and we would go on weekend rides. On roads, with plenty of city traffic. She had a road bike, my brother and I just had more regular cheap second-hand kids bikes, but we never really cared. I've commuted by bike on and off in Sydney, Brisbane, London and now DC.

But I digress. I don't know anything about Florida but honestly 45/55 mph roads would scare me for a regular solo commute (group rides are different) esp with the reputation of drivers in the USA, and my experience with them. 35 mph roads are the most I'll do and even then I try to avoid them.

Perhaps if you could get others to help out with the car $ you could pursue the biking purely as a hobby of your own and commute part-time, and gradually build it up once your parents realize you really enjoy it and get great exercise, enjoyment and satisfaction from riding. This way you can sort of draw a compromise in that you are pursuing biking as a hobby (to begin with, anyway). The car-free folks may have a different viewpoint, but I feel like I still rely on my car for times when I'm too sick or injured to ride into work, or need to carry something really bulky/delicate to work. Often if I'm driving home from work I'll pick up some take-out for the family dinner, since I can't do that as easily on my bike (food gets cold and jostled too much).

You will often be wet from sweat and/or rain when you commute if you ride hard and/or sweat easily (I do). It takes me about 15 mins for me to dry out once I arrive at work. I wouldn't ride in a severe (lightning) storm but there's little else that would stop me from commuting when I'm healthy. Heavy rain slows you down a bit but it's definitely a thrill for me to ride in it - it's refreshing. And right now I'm dying for it to snow a bit or get colder so I can ride on my new studded tires.