The statements "negative thinking feels bad" and "negative thinking feels good" are not contradictory at all, though they may appear so. The way in which it feels bad is obvious, but the way in which it feels good is not, and takes self-observation and honesty to detect. The effort is well worth it, though, because it provides a way out of the conundrum. If I'm only aware of how they feel bad, then negative thoughts are something that happens to me; but once I become aware that they also feel good, I see them as something that I'm doing (or at least acceding to), and I can withdraw that participation.
My experience has been that one has to persist with this concept until the initial indignation ("how dare you say that I'm enjoying this pain") dies down. Then a whole new array of psychological options opens up. It's fascinating. But challenging.
Still the people who never do that are, in honesty, feeling bad not good.
I hypothesize the reason humans perform worse after failing a hard question versus passing an easy question is that by keeping yourself down, you avoid getting into trouble claiming a higher status in the tribe than you can pull off if it comes to a confrontation. But you feel bad so that you keep looking for an opportunity to claim the higher status/more resources position. Perhaps explaining this (if it is true) and that this doesn't confer any benefit in our current environment would be just as effective.
My experience has been that one has to persist with this concept until the initial indignation ("how dare you say that I'm enjoying this pain") dies down. Then a whole new array of psychological options opens up. It's fascinating. But challenging.