to lose an argument despite being in the right; to have right on one's side but still lose
Proverb-like expression describing a situation where logic or justice is on one's side, but one still ends up losing or being defeated in a dispute. Often used to lament the gap between principle and outcome.
In court, you can sometimes lose even when you are in the right.
He made a valid argument, but ended up losing despite being right.
理非 is a noun meaning 'right and wrong', while 理に勝って非に落ちる is a full expression describing the outcome of a dispute.
The expression is composed of classical elements: 理 (reason/justice) + に勝って (winning in) + 非 (wrong/unjust) + に落ちる (falling into). The exact origin is uncertain, but it reflects a traditional view of the disconnect between moral rightness and practical outcomes.