This guy thinks a person is arrogant when he knows nothing about that person and just telling everyone about how arrogant that guy is. So what is the term for this kind of person?
behavior, talk, or display intended to impress others.
behave in a way that is intended to impress or mislead others.
attempting to impress by affecting greater importance, talent, culture, etc., than is actually possessed.
a person who behaves as if they know everything.
irritating as a result of behaving as if one knows everything.
informally, Smarty pants. Reference : marriam-webster
: a person who freely announces personal opinions and judgments; know-it-all, smart-ass The Dictionary of American Slang
I would say this person sounds jealous.
4. Troubled by the belief, suspicion, or fear that the good which one desires to gain or keep for oneself has been or may be diverted to another; resentful towards another on account of known or suspected rivalry:
b. in respect of success or advantage: Apprehensive of losing some desired benefit through the rivalry of another; feeling ill-will towards another on account of some advantage or superiority which he possesses or may possess; grudging, envious. Const. of (the person, or the advantage).