how to use the word "affinity"

The original meaning of "affinity" was connection by marriage. That meaning applied to the relationship between two people, rather than to a particular person, and to the extent that it applied to the individuals, it was symmetric: if one person is connected by marriage to another, then the second is connected to the first by marriage as well. It's therefore logical to use "between" for this meaning.

That meaning expanded to include close association in general, not just marriage, and that expansion retained the symmetry. It expanded further to include an attraction to, and at that point it stopped being symmetric, and "for" became an appropriate preposition.

Dictionary.com lists this attraction for as the first meaning:

a natural liking for or attraction to a person, thing, idea, etc.
a person, thing, idea, etc., for which such a natural liking or attraction is felt.
relationship by marriage or by ties other than those of blood (distinguished from consanguinity).
inherent likeness or agreement; close resemblance or connection.
Biology. the phylogenetic relationship between two organisms or groups of organisms resulting in a resemblance in general plan or structure, or in the essential structural parts.

Unless someone is insisting that "affinity" should be used only with its original meaning, opposition to "for" doesn't make sense. If someone is taking that position, then the preposition is not the only thing wrong with "She has a distinct affinity for music": having affinity is something that the two have together, so it should be "There is affinity between her and music". Which is a rather odd thing to say, because how does music have affinity?