Why are you unpersuaded by a correct argument? Are you saying that you know you have irrational beliefs and are frustrated that people try to reason with you instead of manipulate you?
"Logically correct" and correct argument are oftentimes not the same thing. "Logically correct" but unpersuasive arguments oftentimes starts with wrong model of the world to which they then apply logical rules - e.g. ignores reality, rephrases 60% as "majority" and then proceeds to talk about them as "almost everyone", simplifies long complex theory into something misleadingly simple etc.
Kind of like when they logically explain you that x should be better then y, but you tried both and still remember x being a hell. May sound logical, but you know something is wrong.
I didn't say I was unpersuaded by a correct argument. (Although I'm sure there are circumstances where this happens). I said a lot of people react to a logically sound but badly made argument by further reinforcing their beliefs in the opposite direction, and therefore it's frustrating to see people make that kind of argument for a position I happen to agree with.
