Liǎng ge rén wèile yìdiǎn xiǎoshì chǎo le qǐlai, hùbù xiāngràng.
The two of them started quarrelling over a trifle, and neither would back down.
Tips
usage
互不 "neither ... the other" plus 相让 "to give way to each other". Used for quarrels, negotiations and close contests, where both sides insist on their own position.