Learn Russian: Я никогда не пропускаю биологию.

In Russian, double negatives are required. Whenever you use a negative word like никогда (never), никто (no one), or ничего (nothing), you must also put не right before the verb. Even though it looks like "I never don't skip" in English, it is the only correct way to say "I never skip" in Russian.

Why does the word for biology end in -ю here (биологию)?

It is in the accusative case because it is the direct object of the sentence—it is the thing being skipped. The dictionary form is биология. Feminine nouns ending in -ия change their ending to -ию in the accusative case.

Can I use the verb пропускать to talk about missing things other than classes?

Yes, пропускать is a very versatile verb. In addition to skipping a school subject or missing a meeting, you can use it to talk about missing a bus, a train, or even missing your turn in a game.