Preamble on the logical implication of an antonym
You are trying to confuse people's understanding of the term antonym.
Logically, speaking, the term you could have used is antithesis. However, since all the dictionaries define antithesis as exact/direct opposite, you should use the mathematically more precise term of null-hypothesis
The antonym of good = bad
The null-hypothesis of good = not good <= {bad, not bad but not good}
For the hypothesis
John = good person
then the null-hypothesis of the correlation is
John = anything but good.
In English, it is very frequent for an antonym not being the exact null-hypothesis. In fact, it is frequently true that almost all natural languages have antonyms not being the null-hypothesis. This is due to the absence of a pure binary set of possible states in such cases.
If a phenomenon Z has the possible states sorted by intensity {a, b, c, d}, then we can be sure that
antonym of a = d
But, the null-hypothesis of a = not a = {b, c, d}
What is more difficult when the states of a phenomenon is unsortable or unrankable, then any state within such a phenomenon does not have a generally acceptable antonym.
Therefore, the antonym
Therefore the antonym of the word prefer is indeed among words describing its extreme opposite
- disapprove, disfavour, dislike.
You are asking for the null-hypothesis of prefer, and as I have anecdotally stated, the null-hypothesis of many words is not the generally accepted antonym, due to having non-binary repertoire of states. Prefer is one of those words.
Best Answer
Aura might work, as it has a generally positive connotation. There is also halo, though that might be a little over-the-top in this case, or the more neutral property.