выучить still works in the context
Because you trying to выучить many(some) things not ALL things, so even if you learn those many things you still have a long way to go until you done learning
учить however implies to the process and does not guarantee results, so it would sound that your goal is to try to learn some things but you don't care if you learn them or not
Back when I was a high-school Latin student, we had to memorize "the four principal parts" of every new verb. Just learning amare ("to love") wasn't enough information, but learning the four separate forms amo, amare, amavi, amatus allowed you (in theory) to deduce every single one of the verb's possible conjugational forms, in all tenses, active and passive, subjunctive and imperative, etc.
Russian is a bit simpler than Latin, but generally speaking, for most nouns and verbs there will be 2 to 4 "essential forms" that you need to memorize, not just one form.
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