I don't think it's about single focus because that would be ridiculous of a HC. I think it's more that your background as an offensive or defensive coach is your expertise. We all know these coaches spend hours and hours away from their families obsessing over their craft. McD was a safety when he played, then he moved his way up the ranks on the defensive side of the ball as defensive quality control - DB coach - LB coach - back to secondary coach - D coordinator, etc etc.
So every hour of film, every drill, every fundamental, every OTA, every TC, every game day strategy has been defensive oriented - obviously. He knows how to teach defense. He can spot and recognize real time issues that happen on a defensive play. He can identify areas that need improvement fundamentally on defense. He knows that the DT didn't to X or the LB opened up his hips too soon or the DB took the wrong angle, etc etc.
Of course these men are all wicked smart and they understand offense as they've spent their lives defending against it. But the instincts aren't on that side of the ball and they aren't teachers of each of the positions. I know they can and have knowledge of everything but it's not their expertise.
It's for those reasons I identify a coach as minded on one side of the ball.