"好恶相克的" can be translated into English as "mutually antagonistic in likes and dislikes" or "where likes and dislikes are mutually opposed."
Here, “mutually antagonistic” or “mutually opposed” convey the idea of two things being in direct conflict or opposition with each other, while “in likes and dislikes” specifies that this opposition is related to personal preferences or aversions. This translation captures the essence of the original Chinese phrase, which describes a situation where one's likes and dislikes are in direct conflict with those of another or with some external factor.