Definition: to analyze a subject down to trivial and unimportant details; to obsess over small disagreements, when you already agree on the bigger details
Examples:
I want to give the approval and all you want to do is split hairs about what color the body should be.
We agree on the bigger picture, and we even agree on most details. But I get really frustrated, because he keeps splitting hairs, arguing about really small details that don’t matter.