Let's unpack the numbers.
Whites are responsible for 51% of hate crimes, but they make up 61% of the population. Blacks commit 21% of hate crimes but they make up 13% of the population. So, one can argue that black men are disproportionately likely to commit hate crimes.
In other words, your whole premise was built without consideration of how large the white male population is relative to other populations in America, once you adjust for numbers, the opposite is true.
So, with the opposite being true, why do you think blacks are disproportionately likely to commit hate crimes relative to white men? I ask you this, because I think many of the same reasons exist across all identity groups with respect to causing hate crimes.
Let's explore a possible answer to your question.
Group identity politics is inherently violent. People who identify based on race, religion, or sexual preference tend to perceive that they have been victimized or are threatened by other identity groups.
When people are affluent, they feel "the system" works for them. But when they are struggling to "make it", they feel threatened, whether they are black, white, or Hispanic by competing identity groups. So, they develop an irrational fear of them, which contributes to racism and bigotry. The increase in societal identity politics contributes to this tension.
With blacks disproportionately living in poverty or performing working class jobs, it makes sense that they would disproportionately commit hate crimes. And with whites disproportionately working at upper middle-income "secure" jobs, it makes sense that they would disproportionately not commit hate crimes.
So, if we compare the absolute number of people by race who are defined as members of the "working class" or in poverty, you will see "hate" crimes are pretty proportional. So, blacks are not more likely to commit hate crimes based on their skin color, but because of their social situation.