Students can obtain unlimited private GitHub repos for free via the GitHub Student Pack:

https://education.github.com/pack

Shitty as a high-school student at a school that doesn't have official student emails since they'll just immediately reject my application for the student pack :(

Having to apply for it still sounds a lot less convenient than just using bitbucket where it's free to begin with. What does github offer better besides brand recognition?

UI.

I've used both and the only one I'd complain about is GitHub, especially their terrible desktop client.

Not necessarily. I know a few people who had emailed their ID cards (which had validity) as a proof for student status because they didn't have a student email. You could give it a shot.

They take this away after 2 years. Bitbucket gives students an Ultimate account for free, forever.

Or they could use GitLab which is free software (the community edition). And you can also make private repos without fee as well.

I dont pay for private GitHub repos but I do prefer their UI over Bitbucket's.