I have a mild distaste for anything bitter, but I would certainly eat those foods if I were hungry enough.

Ever since I was a child, I always had a great distaste for bananas, as I cannot stand their texture or their taste.

I wouldn’t say that I hate winter, but I’ve always possessed a minor distaste for the cold and the biting wind.

Saying that you dislike something is roughly equivalent to making a statement of distaste for it.

If there’s one thing that always filled me with a sense of distaste during high school, it was my algebra classes.