I think there's three parts to this.
The first is that white people and black people have a very different relationship to the concept of racism so they're not even close when it comes to identifying it.
White people tend to think of racism along with visions of klan hoods and cross burnings. To most white people, racist is perhaps the worst and most insulting words you can call them. All of this makes sense when thought of in context, the only racism most white people ever experience is on TV.
Black people live with it on a daily basis, so to any black person racism is not some big deal of a topic. It's something that because of it's prevalence in their lives is talked about all the time, and like anything that's talked about and thought about frequently they get to knows it well to the point where there are terms to describe and differentiate even the most mundane things (i.e. microaggressions).
So right here we're already on different planets, if a black person tries to point out something racist a white person did the white person is likely to think they're entire character is being questioned. This is a huge reason why we talk past each other.
The second part is the difference between racism towards the individual vs racism towards the group. This is where the "I can't be racist cause I have black friends" thing comes in and has black people rolling their eyes. You can think highly of any individual black person but when most people identify racism it's normally in the form of an attitude about the black (or any minority) community. You can have all the black friends in the world, but if your attitude towards the community at large is that they're lazy, thugs, or whatever stereotype that's going to impact how you act to the black people you don't know. This is far more important because on a large scale this is what impacts their lives.
The third part is the difference between individual racism and systemic racism. To many people including many white people, believe that the system itself is racist (as in built to favor the cultural norms of white people leading to disproportionate treatment). This leads to charges of racism being taken as some kind of personal attack when it's merely the cumulative result of all our actions.
So I guess to summarize, it's complicated. I personally am more in line with racism defined as the second part as an attitude towards the group. I don't think it's helpful to focus on micro aggressions because they are by definition, micro, which means they can be explained in more ways than one, but the whole klan hood wearing n-word using concept also needs to go in the trash. We've come fast as a society so our ideas on these topics should reflect that progress.