He always spouts sophistry and the conversation never moves forward.
That kind of quibbling won't work.
屁理屈 is a flimsy, sophistic excuse dressed up as logic, the opposite of 正論, which is a genuinely sound and fair argument.
sophist; quibbler; person who argues with twisted logic
Compound of 屁 (he, 'fart') and 理屈 (rikutsu, 'logic, reasoning'), literally 'fart logic', implying worthless or twisted reasoning. The exact origin is uncertain, but it is a colloquial coinage.