1. The girl’s mother asked what time they got home and the girl told her 10:00. The brother insisted that it was 10:05. The girl told him he was splitting hairs and that five minutes didn’t really make a difference.
2. We can’t seem to agree on this minor point, but I don’t think it’s worth arguing about. I’m not going to split hairs with you about this.

The expression suggests that a hair is so thin that it would be pointless to try to split it. Similarly, it is pointless to argue over details of no consequence.