I think the idea of positive discrimination is related to countering inherent bias.
You might think A isn't as qualified as B. But it is known that inherent bias against A is very likely. So you might decide, even though I believe B to be more qualified, I will go with A, knowing that my judgement might be wrong, because of the likelihood of inherent bias.
In a way, yes, the known biases, can create a new bias. I bias against my known biases. This does mean that at an individual level, I favored someone else, when I initially wouldn't have. But does it result in better outcomes? I think this is where it matters. Let me explain.
If one is chosen and given opportunity over another. That choice is always going to be judgemental and opinionated. You're trying to predict who will make better use of the opportunity and contribute back the most for being given it.
But predictions, like in machine learning, show that a biased data set often perform poorly. So I think part of positive discrimination is to say, diversity could actually yield better results. Yet, because we don't have diverse data, we don't know for sure. But its still okay for the person who chooses to be of the opinion that it would. I find that no different then saying, well I felt they were more knowledgeable. All of it are intractable metrics in an attempt to predict outcome.
Edit: Some more thoughts related to fairness. Is it fair to give opportunity only to those who would maximise it? What if it was true, that there was a genetic quality, sex, or race, or a more specific one, like height, IQ, EQ, etc., which was the key variable to maximize the opportunity? Is it fair to say only they shall be given such opportunity, always? Or should we pick at random? Would that be more fair? Are there other scheme? What does it even mean to be fair? Your genetics aren't fair, should society be fairer then them? Clearly in the modern western world, we seem to define fairness as, whoever can maximize the opportunity the most, shall be given it. Aka, meritocracy. Is this best for our society though? If so, are we doing a good job at it? What if we try to do that, but instead have been giving opportunity to those who most resemble us? Not to those who can most maximise it? What then? Is that unfair?