"Privilege" is often misused. It's supposed to be a way of pointing out the advantages a person may have due to a particular characteristic they share with the majority of people in their country. Instead, people on Tumblr seem to be using it as a way of calling people assholes for things they can't control (ad hominem, etc). "Privilege" is often twisted to mean "you have something I don't, and I want it - or at the least, you shouldn't have it anymore." This is a bad form of social justice and is closer to communism than justice.
If you believe white privilege exists, that can actually be considered a form of racism if you want to be technical about it. Remember the definition of racism? "A belief or doctrine that inherent differences among the various human races determine cultural or individual achievement…"
So by claiming white people have extra advantages in society due to their skin color, that would be racism. Ironically, a white woman came up with the idea of white privilege; unfortunately, she didn’t use any actual evidence to support the claim that her skin color gave her societal advantages.
I’m not going to talk much about white privilege much because people haven’t decided yet if it even exists in first-world countries. There’s evidence both for and against the concept. Are white people, in general, better-off than non-whites in certain areas? Possibly. However, you can’t discount individual experience or historical implications in order to claim “white privilege” exists, which I often see people do. People experience life differently and you can’t apply blanket terms like privilege without regard for that. You also can’t ignore thousands of years of history and culture to suit your own beliefs.
"Privilege" in general can be considered a bad argument, mostly because privilege applies to what is perceived to be the “group in power” - which means privilege essentially goes away if a privileged person goes to another country where they would not normally have privilege. If a country is primarily composed of one race, it stands to reason that they would be afforded certain privileges as they are what’s most common. Is this right? Not really, but that's what seems to happen. Literally everyone has privileges. In the USA; white people are becoming a minority so “white privilege” may not even be a thing here (if it does exist) in the future. Globally, white people are approximately 15% of the entire population, so if you take world population into account then white people aren't the majority and therefore white privilege is not a global concept. "White" is also extremely vague and erasive, as people who appear white may not actually be "white" in some contexts (for example ethnically Jewish people). In most countries, race relations are nearly irrelevant in the face of ethnic relations.
The concept of privilege doesn’t necessarily illustrate societal issues. While it can, it’s mostly about arguing and philosophizing, which isn’t always productive. This isn’t even taking into account that literally everyone on the planet has at least one “privilege.” Privilege can apply in good or bad ways, and it can be argued that the concept itself is not harmful.
One example of white privilege in the USA: The New York Police Department's "Stop and Frisk" program, which was deemed unconstitutional and ineffective when it was revealed that mostly non-whites were stopped by police officers. (A personal account from someone here.) There's also clear discrimination in prison sentencing and arrests.
For more examples, there's a short 17-minute documentary on Youtube called "True Colors - Racial Discrimination in Everyday Life" (part one) (part two)
A comment I found on this concept:
I consider "white privilege" to be a politically correct euphemism that is meant to encompass a view that would more accurately be defined as "minority disadvantage". The problem though, is that what is defined by "white privilege" should not be considered a bad thing, we all want every member of society to grow up in a safe environment which encourages positive values, good opportunities, and results in a perception of inherent dignity. White privilege isn't something anyone should apologize for; minority disadvantage is something we, as a society, should work together to overcome. Using a politically correct term that doesn't accurately represent a problem does nothing to address the actual issue at hand, and ultimately does more harm than good.