Positive discrimination has no place in an ideal world.
We are not, though, in an ideal world. The system as it existed for a very long time was so heavily biased against minorities, and even while that bias isn't nearly so deep-seated, the problem now is more one of inertia (as well as the almost impossible to solve problem of unconscious bias). Positive discrimination is designed to try and fight this inertia, not by sacrificing standards to get the job in the first place, but by increasing the chances for a suitably-qualified member of a minority to get employed.
The resentment that results is, I think, the product of misinformation. Every time this comes up people say "It should be the best person that gets the job". They are of course correct to say so. But why are they so convinced that this is being sacrificed? Changing the order in which applications are considered, or trying to eliminate/ expose/ work against unconscious biases, or holding recruitment drives that widen the application pool, don't change the end result that you are seeking the best person for the job.
Why, too, is this attitude never reversed? Do those who complain about positive discrimination ever wonder why the "best person for the job" is still massively more likely to be a white man in most cases than you'd expect given the demographics of this country?