also: りをもちてひにおちる
lose an argument despite being in the right; have right on one's side yet succumb
Proverb-like expression meaning that even when one's position is logically or morally correct, one may still lose the dispute or be defeated. Rare and somewhat literary.
Sometimes you can lose an argument even when you're in the right, so strategy is also necessary in debates.
理詰め means arguing purely through logic, while 理をもって非に落ちる describes the ironic outcome of losing despite being right.
負けるが勝ち is a proverb meaning 'losing is winning' (sometimes it's better to concede), whereas 理をもって非に落ちる focuses on the injustice of losing when you are correct.
Standard kanji form using 以って in kana.
Alternate spelling using the kanji 以て; less common.
Archaic reading もちて for 以て; very rare.
A set phrase combining 理 (reason, right) + をもって (with, by means of) + 非 (wrong, injustice) + に落ちる (fall into). The exact origin is uncertain, but it reflects a classical Chinese-influenced construction.