I agree that it's not necessarily irrational to feel, but I think the way we feel is clearly irrational. For example, our emotions don't seem to work in a time-consistent manner, and we often later regret actions that we take based on strong emotions, when those emotions eventually fade away. If we could modify the way our emotions work cheaply and safely, I think many of us would probably take advantage of the opportunity. A rational agent wouldn't wish to modify its mind like that.

Here's another, more specific example. I sometimes feel a sense of schadenfreude when someone that I might be in status competition with publicly makes a mistake or suffers a setback of some kind. By itself, this feeling may not be irrational (except perhaps on a group level), but I simultaneously feel a disgust for myself for feeling this way, and wish that I could edit away this ugly emotion. (Until then, I have to spend some effort to keep myself from being overly critical of others.) Would anyone claim that these emotions together do not constitute irrationality?