When getting into discussions about things like affirmative action, feminism and general identity politics, I find that the topic of privilege comes up a lot. White men are privileged, which is why they are at the top of society or in power in various positions. They have privileges to which they are blind, and to combat this, programs like affirmative action are necessary. Suppose we take this as a given, that white men are privileged over everyone else. There are, however, no laws which explicitly privilege white men over other groups (at least as far as I know). There are no legal disputes which hinge on the color of the skin as a matter of law. The privilege that white men enjoy is not an institutional privilege. It is not codified in the rules at the legal institutions, or in any major institutions generally. Instead, privilege must be social or cultural, not institutional.
First, let me be clear: whites most definitely did benefit in the past from institutional privileges, and it would be stupid to think otherwise. Slavery and Jim Crowe laws are clear examples of this. Whites were given advantages in laws and rights. Today, there are no such laws that make this distinction between whites and blacks. Whites are no longer institutionally privileged. The privileges that white men have are therefore cultural and social. Cultural and social privilege is very hard to correct, and I'm not sure that anyone really knows a good way to go about it.
Cultural privilege is something that cannot be corrected institutionally, because it will create backlash. Affirmative action tries to combat the socio-cultural privilege of being white and male with an institutional privilege and preference for other demographic groups. This, instead of making the problem better, creates additional cultural privilege for the white men. Why? Because the white men who made it managed to do it without help from the system. Everyone else? They got help. They couldn't hack it on their own merits. This new white male privilege now exists because they are viewed as having achieved, as making it through an institution that is biased against them.
You see some of this happen in the tech industry nowadays, with articles saying that white men are privileged for being taken seriously for their achievements. The problem is that the proposed solution just makes that problem worse. Creating institutional privileges for the 'underprivileged' just give the culturally privileged additional privileges.