Racism is something practically every POC (person of color) deals with. Sometimes it's a "small" thing, like cultural appropriation, where people get unhappy. Other times it's a big deal, like hate crimes and xenophobic mass shootings, where people die. Many white people understand the concept of racism, and that when they are accused of being racist, it's just a POC saying that they feel hurt. Many white people go on to understand that a POC has the authority to decide whether something was racist or not and whether they felt hurt or not, because it is their culture and their feelings. A lot of the time it's an accident; it's not like a white person actively wanted to hurt a POC. It's like when you're walking down a street with a friend and step on their toes - you probably didn't do it on purpose, but your friend still has every right to say "Hey my toes really hurt, please apologize and don't do it again."
Unfortunately, due to the aggressive reactions that xenophobes and right extremists have, when someone calls them out for racism, POCs often have to resort to extreme measures to make themselves heard. Usually, if you step on a friend's toe and they say 'ow,' your first reaction is not "You idiot! Why did you put your foot on the ground for me to step on! What is even wrong with you?! Couldn't you see that I was going to put my foot down there?!" Which is why POCs have to sound like broken records and talk about "black lives matter," "white privilege," micro-aggressions, cultural appropriation, etc.
Mira Jacob recently posted "A Flowchart For People Who Get Defensive When Talking About Racism" to Buzzfeed. Many who read it, including myself, thought it was overly sarcastic and offensive in many ways. When a POC accuses a white person of racism, it's not meant to be a personal attack (which is what Jacob's in a way wrote); it's meant to show you how to be a more considerate person and recognize that there are certain flaws in the system that eventually need to be changed.
So here is my simplified version of a friendlier flowchart, for anyone and everyone, to understand what went wrong and how they should react to being called a racist.