If I'm having some kind of internal experience that may color my interpretation of what my interlocutor is trying to tell me, I feel like I owe it to them and whatever we're discussing to stop the conversation as soon as I realize something is wrong, since if e.g., it turns out I'm sleepy, taking a nap wouldn't (I think) be sufficient to fully counteract the negative opinion of the topic I formed when I was crabby.

Could you give an example of a graceful exit? For me, interrupting a conversation without saying why I'm actually doing it feels dishonest/rude, especially if we're discussing something that's important enough for me to care that I treat it fairly.