Where is my damn privilege I so often hear about? Why can't I feel it?
I think there's a lack of nuance in many of these debates. Some argue about race or racism with the classical idea of the word in mind, a pure racism in which you believe racial characteristics should give legal rights (or absence of them). An individual feeling of superiority, e.g. equating the worth of an African and a dog or an Eskimo and a seal.
Others argue with another understanding of the word in mind. Racism can be present in a society even if no one in that society would describe themselves as such. Perhaps you can call it institutional racism. This is today's white privilege in many countries. If you're name is Ahmed, you're less likely to get hired over a John with identical qualifications. If two cabbies are waiting for a customer, the likelihood of picking the white guy driving is higher than the black/brown/whatever. The probability of getting pulled over by the police, audited by the IRS, not believed in a word against word situation. An implicit bias that's a bit hard to deny exist. However, these examples are all related to norms rather than laws. By law we're equal, thus there's no institutional classical racism.
It's possible to argue whether this should have a different name than racism, but it won't change the reality . It's also possible to argue (a lot) about why this is the case. Is the proper explanation group thinking, xenophobia, inherent flock genetics, some other cultural bias, the press or whatever. I'm sure a lot of social scientists has written extensively on this topic if you're interested.
One common counter-argument is that all these implicit biases exists to some extent for everyone. A Harvad grad is more likely to hire a fellow alumni rather than an evil from Yale, or god forbid a British educated moron. However, some groups (perhaps African Americans in particular) suffer from this bias in a lot more situations than others. I don't think it requires a lot of empathy to understand how one might feel if you go through life being discriminated against at every turn, whether it being through law or norms.
A lot more can be said, but the notion that no one are able to explain the idea of modern white privilege is wrong.