Racism is a difficult topic to address, due in large part to the fact that it tends to polarize the conversation in one direction. Usually when the word 'racism' is used it immediately refers to someone who is white harassing or patronizing someone who isn't. Now while I won't argue the fact that being 'white' does offer privilege, the default setting for what most people consider 'racism' is inherently racist. Perhaps a few examples would help illustrate my point better.
I was raised to NOT be racist. I know that's not the case for all white families, but that was my upbringing. I also grew up in a predominantly white neighborhood until I moved to the south to attend college. Upon arriving in the south I had little concept of racism and just generally thought 'people are people, this'll be fun to gain new perspectives.' However, as I started greeting people who weren't white, especially black people, I noticed a strange trend; a lot of them either acted surprised I was speaking to them or would offer up one of those phony disarming grins that are usually reserved for used car salesmen. A lot of them didn't, as well, mind, and I had some good conversations with those people, but the general, I dunno, distrust? I received just as a consequence of my 'race' was unusual to me because I didn't think in terms of 'race' I thought in terms of complexion.
I got used to that eventually, however, and soon I was making friends of all stripes, complexions and backgrounds, but then came the really weird thing that totally freaked me out; white racism committed by white people. There's a guy who went to the local LGBT center I used to chill at a lot, and he was half white, half native american, but it was hard to tell just by looking at him. Unless you had extensive exposure to native american culture/people (which I did growing up in Utah), you'd just think he was white. Anyway, he would crow from the rooftops about being Native American all the whilst completely deriding white people. It was common for him to walk into the room and point-blank say something like, "white people are evil." Shortly thereafter everyone who is by all accounts of 'race' (I'll detail that more in a bit) 'white' began digging up any ancestry they had that wasn't 'white' and crowing it from the rooftops, as though being white is some kind of disease or disability they didn't want to catch.
Now I am well aware of 'white privilege' and I do everything in my power to ensure my little corner of the world is as free of it as I can possibly make it, but did what that guy do piss me off? Yes, yes it did. I put A LOT of effort into paying attention to my non-white friends, listening to them, their concerns, and learning common socioracist pitfalls established by white privilege so that I can avoid them all because a bunch of ancestors, whom I'm not even related to, decided to be jerktards to non-white people for a few hundred years. It's REALLY freaking annoying.
Does all that mean I am as discriminated against as say African Americans? No, it does not, but it does mean that 'white racism' exists, and it causes a lot of stress for white people who already have to deal with the constant guilt laid on them for actions they had no influence over perpetrated by ancestors they had no control over and may not even be related to. So when you see white people getting edgy and defensive, that's most likely what's going on, unless they actually are racist, but that's a whole other discussion right there.
Furthermore a lot of people forget that 'race' does not actually exist. 'Race' as typified by skin color, is a social aberration created by humans to 'other' people different from themselves. The level of biological separation required for humans to occupy different races simply does not exist. Complexion and minor physical adaptions such as nostril width and eye positioning, do not warrant reclassification of humans into various subspecies. Black people do not have a different genome, nor even phenotype than white people, they merely express various facets of the same genome and phenotype to different degrees. In short, 'race' is an artificial construct created by insecure individuals to separate and/or stratify themselves from others. The sooner we can get that through our heads at a social and cultural level, the better.
I guess what I'm saying here is, "I do my best," and I know I'm not alone. And if some self-righteous 'anti-racist' crusader decides the best way to address racism is by punking white people with their own ignorance, we're never going to make any progress. Crap like this 'exercise' will only serve to further alienate people from each other and deepen the racial divide. We should be focusing on common ground and understanding, not forcing peoples' own ignorance down their throat, that's never solved anything.