Right now, there is no way to see which tags a user downvotes often, just which tags they upvote / use often. Relatedly, there's no way for me to see which tags I've downvoted at some point (but might have changed my mind on).

For example, http://musicbrainz.org/user/reosarevok/tags doesn't show "americana" at all, but I have downvoted "americana" once - so it should be possible to see that (in a separate view for downvotes).