I recently read an article on Bleacher Report that compared the Duke and Kentucky programs. The writer concluded that while Kentucky has a more rich basketball tradition, they haven't matched Duke's success over the last 25 years. He was insight, he used logic and statistics, but he was criticized nonetheless. Why? Because people hate Duke basketball.
Duke basketball is not the most dominating program in the history of college basketball. They aren't even the best program in their area. No, much to the chagrin of Duke fans, North Carolina is the superior program. With the exception of the early '90s and early 2000s, they always have been. One of the reasons for the hatred of Duke has to be their own fans' false sense of basketball superiority.
That being said, there are things at which Duke is just plain better. They are easily the best academic powerhouse in college basketball. Stanford is often good, and UPenn used to be good, but no other elite academic private school has competed with the big boys as well, or as often, as Duke. This may make fans of bigger schools angry (and make no mistake, Duke isn't the only school who graduates players), but it is the truth.
They have also maintained a level of success over the last 25 years that nobody else has matched. With the exception of 1995 and 2007, every Duke team has competed for an ACC championship. No other team in college basketball can make that assertion, regardless of conference.
Another reason for the hatred of Duke is their treatment by the media. This is actually one of the biggest misconceptions fans make about college basketball. Duke basketball is a lot like Notre Dame football in that they are always being talked about, but the talk is often far from positive. For every Dick Vitale, there is a Joe Linardi. The media loves to beat Duke when they're down just as much as they like to praise them when they are winning.
Recently, the criticism of Duke is that they have too many white players. This kind of criticism has always been astounding to me. For a society that prides itself on not letting skin color impact the way we view people, it sure doesn't carry over to sports. A white guy can play point guard just as well as a black guy can play quarterback. Race doesn't matter, and those who point to this are enforcing a stereotype that only serves to embarrass themselves.
The real reason why people hate Duke is that they are jealous. I know many people who dislike Duke, but rarely do I hear a compelling argument for why they "suck." During Mike Krzyzewski's tenure at Duke, he has run a super-clean and ultra-competitive program. If you have a problem with that, suit yourself, but don't pretend that you have legitimate reasons; because you don't.