Both of you are right and wrong, it's not so black and white.
You absolutely can make friends, chat with people at the bus stop, strike up convos at bars, the local ski resort, bike park, etc. Friendships can naturally blossom into relationships (or remain friendships, which is healthy and natural too).
You can't approach people and immediately ask them out, it feels weird and unappreciated (and that goes both ways, I've had a complete 180° role reversal and it was still weird and gross).
You're young, you have plenty of time, and honestly the weirdest thing about all this is that your parents are worried you're gay, like there's something wrong with that. There's barely any differences between genders, people overhyped the shit out of it in church, tbh.
Anyways, any% dating really doesn't work, and I feel like your parents should know that. Don't even try for dating, everyone can sense desperation. Just dgaf and focus on having fun and making friends. Love will naturally evolve out of good friendships.