"I do not do what they want, but what I want."
Translation:אני לא עושה מה שהם רוצים, אלא מה שאני רוצָה.
Because then it would be an incomplete phrase. אבל means but as in “I like carrots but I don’t like pears”, whereas אלא means but as in “I don’t like pears, but (rather) apples”. You can see אלא as a sort of “instead”.
So here if you use אבל, you’d need to follow up the phrase with something else. Eg. “I don’t want what they want, but what I want [is not available]”.
We don't usually add formal answers to the database. You have every right to use formal language in the "Formal" skill, but throughout the rest of the course you should try to use standard language, since we're teaching Modern Hebrew on this course.
The second phrase would not be complete. אך is the same as אבל in grammatical function. אלא has a different meaning, of "but rather".