I think that Bush was sincere in his belief that bringing democracy to Iraq was a (if not the) primary goal of the Iraq War, and that doing so would be beneficial to the Iraqis. And I could believe that he felt a "white man's burden" and obligation that, because he could do so, he ought to do so.
[And to be clear: my belief is that the notion of "white man's burden" is incredibly racist and offensive, and I do not condone actions taken in such a manner.]
While I wouldn't call it "allergic to democracy", I can also entertain arguments that successful democratic regimes have preconditions for their success that Iraq simply did not have. I can even entertain arguments that democracy is not the best form of government, and it strikes me as mildly offensive to presume that democracy is automatically better than whatever form of government exists.
I think OP's point is that the Iraq War was undertaken in the [racist] belief that they were bettering the Iraqis by bringing democracy to them, and the failure is that, well, we were racist in the first place to believe that "bringing democracy" to another people is "bettering" them.