Because they win but that effects all winning teams in the end, Yankees, Cowboys. Though I know many in North Carolina were for Duke, I do think a lot of NC fans are against Duke.
Some years ago, I found websites of people who had this disdain for Duke, check out this book. It's not hard to find to track down this dislike, I once found a website I believe with that same name. I'm neutral myself.
Tarheels fans, yes, that is a lot of the anti-Duke sentiment but of course, not all of it by a longshot.
The Duke hatred is a breed apart from all the other haters. And almost no one in NC pulls for Duke. They’re not even close to as popular in their hometown as UNC is in Durham.
Tiny school. Small fan base. To say they are an “empire” like the Yankees or the Cowbosy - both of whom have massive fan bases - and massive resources - is just absurd.