For the record, I am white, and always checked the white box on my application forms. I believe it would have been irresponsible for me not to. By being silent on the subject of my race I would have been denying that race matters (not just in American society, but in every society). In effect, my silence would be a vote in favor of the status quo.
There are lots of reasons why race stats are important -- they allow us to monitor very real disparities (in terms of education and income level, incarceration rates, etc. etc.). Why do these disparities exist? Since no-one here is explicitly suggesting the innate superiority of one group over another, it would appear to reflect an uneven playing field. Indeed, no-one here denies that racism exists. However, some whites argue that if we ignore it, it will go away (how long are you willing to wait?), that things are already moving along nicely (most minorities would not agree), that people are masters of their own fate.
By couching the debate in terms of "equal opportunity for all" you are actively perpetuating the lie that there is an even playing field to begin with. There isn't (as Paendrag already acknowledged). Whites are clearly privileged in all facets of society. Whites have always had affirmative action! When whites succeed, they should acknowledge that they benefit from historical circumstances and their majority status (effectively, the power to define reality). Sure, hard work is important, but if it were truly the only determiner of success, the current inequities simply would not exist.
When one group begins from a privileged position, equal (i.e., undifferentiated) treatment of all groups does not constitute fair treatment.