Is self-infallibility a mental disorder? I realize all people have various and complex biases, and that we all get into arguments from time to time. However, I've known one or two people who seemed abnormally resistant to suggestions that they might be mistaken. Their tendancy to distrust and argue seemed to impair them socially, to the point where they struggled to maintain relationships. This makes me wonder if "self-infallability" is ever actually a mental disorder.

Is there a mental disorder associated with being severely argumentative or otherwise "self-infallible"? Especially if it impairs one's social or academic skills?
I've not seen self-infallibility listed anywhere; however, there are a few psychological constructs that may be useful:

Dark Triad
DSM5 - Conduct Disorder
DSM5 - Narcissistic Personality Disorder
DSM5 - Antisocial Personality Disorder

Overconfidence may be a synonym for self-infallibility in the context you are thinking.  Overconfidence would normally be thought of as a component of narcissism.
More information would probably be required to distinguish between the four identified psychological constructs but hopefully these four links are a starting point for further research.
References
Jones, D. N., &amp; Paulhus, D. L. (2014). Introducing the Short Dark Triad (SD3): A Brief Measure of Dark Personality Traits. Assessment, 21(1), 28–41. https://doi.org/10.1177/1073191113514105