I took a debate class in high school and we had to give presentations / impromptu speeches all the time; I must have given 20+ speeches that semester. One week, I gave a 5 minute speech on why UNC needed to move on from Matt Doherty and hire Roy Williams. I provided some visuals to demonstrate the poor antics of Matt Doherty while coaching from the bench (stomping on the sidelines after a call he didn't like, walking 5+ feet onto the court, blowing up at refs), and I talked about some of the confrontations he had with players, especially Rashad McCants. Of course you can't forget the lone NCAA Tournament in 3 seasons. Unacceptable for UNC standards.
Carolina needed to move on from him (this speech was during the middle of the season). And Roy Williams had a proven track record, was well respected, and connected with his players. And wouldn't you know it, he was hired maybe a month later.
Loved to root against Carolina and make fun of Roy from time to time, but he was an absolute homerun hire. Before Roy stepped back on campus, Duke had beaten Carolina 12 of the previous 14 times. I can even remember Kenny Smith talking about the rivalry at one of the NBA drafts (sometime between 2002 and 2004) - and Barkley chimed in and said something to the effect of, "Well, I don't know if you can say it's much of a rivalry anymore." Honestly, Maryland felt like a bigger rival than UNC in the Juan Dixon/Steve Blake/Lonnie Baxter years. Roy greatly helped to re-ignite the fire of the Duke-Carolina rivalry.