Reverse racism doesn't exist for the same reason reverse sexism does not exist: they are not opinions or attitudes; they are ingrained systems in our culture which favor one group or class of people over another. It is an imbalance in power such that if you are a member of the group in power, you enjoy certain levels of respect and accommodation that is not available to those that don't look or live like you do. You are subtly favored--through no direct action of your own--over and above others. From birth. It can have effects over where you live, how you are schooled, the quality of health care you are offered, types of jobs you are considered for, and much much more.
Anyone can have prejudice, but that isn't racism. Racism is prejudice + power, and therefore only people who possess that power can be racist.
Repeating for those in the back row: There is no reverse racism (meaning black people CANNOT be racist against white people in our society). There is no reverse sexism (meaning women CANNOT be sexist against men in our society). This isn't a preference, it's a system that is all around you; and whether you want to or not, you are a participant in this system. What you do with your role in this system is vital, and telling... Where you focus your thought, your means, your energy dictates whether you empower this system or help to dismantle it.
I am far from perfect. Like all of us, I was born into this same system, and I also happen to be on one of the higher rungs of this ladder of power. I grew up surrounded by subtle and overt messages affirming my place of power, as well being reminded of all the rungs above me by people who can and have tried to reinforce my "place" on it as a woman, as a member of the middle class, etc. I wasn't always aware of what tools were given to me and not to others, and I like to believe I am on a path to better understanding these tools and how I can use them to help people on the lower rungs get a leg up. Not because I am a savior, but because fuck that ladder...