Or, rather, why the people who state that are usually wrong.
So this definition for racism was brought up again recently when yet another person claimed we live in a post-racial society. Which is usually the context it's brought up in: someone claims Racism = Prejudice and then declares minorities need to get over themselves because of their evidenced prejudice against white folks; and then someone more educated on issues of racism seeks to correct them (using R=P+IP to disprove R=P). I certainly don't believe R=P, but rather my point of contention is a meta issue about how R=P+IP is presented. That is, the theory of R=P+IP as it is customarily presented online is false, even though I do believe something similar is in fact true.
Why it is wrong comes down to one simple fact: there is no Institution. There is no single power structure in which we're all embedded. Even if we parameterize IP by country (as people often do), it's still wrong because there is no single power structure for the entire country. By stating R=P+IP there is an implicit theoretical belief in this singular notion of IP. And as if the implicit theory isn't enough, people often feel the need to be explicit about it. It is this totalizing discourse which is wrong. In addition to being inaccurate, totalizing claims transfer the problem of racism from individuals and individual actions to some external and ineffable "Institution" which individuals are not able to affect (due to its externality). So in addition to being inaccurate, it also serves to dissuade people from altering their personal actions in hopes of combating racism.
The fact of the matter is that we are, each of us, embedded simultaneously in multiple different and often conflicting power structures. I am not only in America, I'm also in Bloomington and I'm also a graduate student. (And anyone who thinks academia isn't a power structure orthogonal to real life is seriously misled.) More to the point, prior to moving to Bloomington I lived in Baltimore for two years. In Baltimore they have problems with racially-motivated black-on-white hate crimes. Now, when I can be hospitalized or killed for the crime of riding the bus while white, anyone who says it's merely "prejudice" has some very odd definitions rattling around in their head. In Baltimore, yes, blacks can be racist too. So when someone gets on their high horse and starts making totalizing claims about how the general disenfranchisement of blacks in America means they can't be racist, it's my turn to call them out for spouting bullshit.
My time in Baltimore was thankfully free of any (noticeable) racism. And I'm sure most other white residents receive less racism from blacks per annum than the average black person does from whites in most places. This isn't the oppression olympics, but rather it's an existence proof: When I was living in Baltimore there were numerous white people hospitalized and killed due to being assaulted on the bus by blacks because of their race. This happens in spite of the fact that everyone living in Baltimore is also living in America where blacks are typically the targets of racism. These two different kinds of hatred stem from being embedded in two different systems of power. In America whites have more power than blacks and use that to police racial borders. In Baltimore, which has different population dynamics (e.g., blacks aren't a minority), blacks have more power than whites and will use that to police racial borders. There is nothing about the power dynamics of America as a whole which precludes some part of America having opposing dynamics.
So IP is not a constant, nor is it a function only of the country. For the R=P+IP equation to be true, IP must be a function which takes in all the different power structures we live in and highlights whether any of those structures provide power in the given context. Whether my power as a white person in America or my weakness as a white person in Baltimore is more relevant will depend on the situation and is not simply the sum of the power from all structures. Similarly, whatever sorts of power I have as a graduate student are unlikely to be of any relevance in contexts that have nothing to do with education. Institutionalized power is both polysemous and contextually dependent. What is institutionalized in one structure need not be institutionalized in others, and which of these many "institutions" can be brought to bear is constantly changing.
By trying to totalize over these two dimensions, people prone to espousing R=P+IP as if IP were a constant are not only misleading those they are presuming to educate, but in so doing they are also failing to acknowledge that individual institutions can be changed, as can the dynamics of which institutions affect our lives. Institutionalized power can never be entirely eliminated. It can, however, be restructured so that it does not support the marginalization and oppression of racial minorities (or women, LGBTQ, disabled people, etc). And most importantly it is because of our own power within these different systems that we are able, through personal actions, to alter the systems in which we have power. We don't have racism because Those People Out There all got together and agreed to it; it is because our personal actions are complicit in preserving the institutionalized structures which support the oppression of minorities. But those very same institutionalized structures give us the currency needed to alter them; it is not enough to want equality, we must have the power to obtain it.