This isn't actually new; I've seen articles about this study since
2011.
It isn't difficult to understand it, I don't think. We live in a highly segregated society, where it is easy for white people to not witness anti-black racism. If you are a white person who doesn't ever see anti-black discrimination, and who interprets attempts at ameliorating existing barriers, such as affirmative action programs or diversity goals, as evidence of anti-white bias, it's easy to see how there are white people who mistakenly believe that anti-white racism is a bigger issue.
This is one of those times where it is appropriate to talk about privilege. In this case, a white person who believes that anti-white racism is a bigger problem for white people than anti-black racism is for black people is making assumptions based on their experiences as a white person, experiences which are effected by their racial privilege that largely insulates them from issues of racism. This means - quite naturally - that they have a skewed understanding of racism, which causes them to misunderstand and misinterpret programs designed to address racial inequality.
The solution there is pretty simple - that person should step back from his experiences and instead look at more objective measures of discrimination faced by black people.
I have family members who are convinced that anti-white discrimination is dire, and it's completely connected to their unwillingness to look outside their own thought processes and sets of assumptions to see that their experiences might not be relevant to a particular discussion, and might even lead them to incorrect conclusions about the experiences of other people.