Well, the problem is that it is very much more. The recent outcry over Harvard's President's words on women and math is a very lucid example of how negative stereotyping can really harm people. I mean, really, this paragraph says it all:
The power of stereotypes has been documented by psychologist Claude Steele on "stereotype threat." Certain groups - such as African-Americans and women - can suffer a burden of anxiety because they are aware of the negative stereotype of the group to which they belong. When they are told that women aren't good at math, women do much worse on a test than when they are told nothing at all. Without the negative information, they score nearly as well as men.
But the example of women being not supposed to be good at math is very minor compared to much of the negative stereotyping that goes on in the police forces.
I spent Martin Luther King Jr's birthday (and the day before) at two events highlighting the African American community. The second was about Police violence, so it's no surprise that the police negative stereotyping of african americans came up (btw, I recommend everyone listen to Dr Brossard's speech, it's a very erudite look at the history of such things). But the first was just a celebration of the Reverend King's spiritual life and his civil rights look. And every African American who took the podium for their monologue mentioned that they had been targetted by the police because they're black.
Even random stupid sit-coms make jokes of the fact that a black man will be stopped by police for no good reason. Folks, this is not a healthy society when a large percentage of our people are made to feel like they should be doing crime! Or they should be looking like a ho. Or they shouldn't be good at math. Or any other negative stereotype that is applied to any group of people. And I'm sorry, but I don't find it funny.