Yes, it's wrong.
The hints system gets confused easily if a given word occurs somewhere else in the sentence already -- in this case, there is a "for" in the correct translation (as the translation of für) and I suppose that's why it brought "for" to the top of the list for gegen as well.
But that's not what it means here.
The ordering of the hints is not completely reliable and so they can never be "suggestions" or "recommendations" -- in the end, you have to rely on your own knowledge. (Either because you knew it already, or you try it and get it wrong and see the correction and then you learn it.)
Because it would be much more likely to be contrasting two prepositions applying to the same person ("for her or against her?" or "for them or against them?"), than the change the preposition and the meaning of the pronoun at the same time ("for her or against them?").
the plural gegen
What about when you are talking?
Then you usually have context -- have you just been talking about a woman ("her"), about several people ("them"), or about the listener ("you")?
Without context, you can't tell the difference in speaking between sie (her/them) and Sie (you).
In a previous lesson, I think we were taught: her = ihr. Why 'sie' is used here?
English has merged the dative and accusative cases into a single objective case, while German keeps them separate.
So "her" can be either ihr (dative) or sie (accusative) in German: ich gebe ihr ein Buch (I give her a book) versus ich sehe sie (I see her).
Also, "her" in English is also used for possession; the translation for this happens to be ihr as well ("her book" = ihr Buch).
So "I buy her water" (Ich kaufe ihr Wasser) is ambiguous in both English and German, between "I buy water for her" and "I buy the water that she sells". (The masculine equivalents would be "I buy him water" and "I buy his water".)
"sie" is nominative and accusative, 'ihr' is dative. Here's the full table: https://en.wikibooks.org/wiki/German/Grammar/Pronouns