Don't see what the big deal is. The slide refers to spearheading a diversity program, not the company itself. Seems intuitive to me that such a program with only white, male managers might be problematic.
Your use of "only" is undeservedly generous of the attitude reflected on that slide. Furthermore, the slide actually doesn't even really address gender as a reason to disqualify someone, just race. They aren't talking about having a diverse group of people, including white males and females, leading diversity. Instead that slide near as I can tell communicates a policy of excluding white people.
Furthermore, I don't understand the racist attitude that somehow white or male people are somehow less qualified to lead a diversity program. Interpersonal skills, knowledge of the myriad diversity initiatives and approaches tried elsewhere and how effective they have been, knowledge of hiring practices, knowledge of recruiting practices, knowledge of retention practices, knowledge of the law surrounding hiring, recruiting and retention practices, professional network, etc. are all the type of things that should be relevant when choosing the most qualified candidates for such a position. Discounting all these and elevating someone's race and gender to utmost importance is blatantly racist policy/attitude.
What about experience? If nothing else (and there is else), it's reasonable to think that someone from a group which has been discriminated against may have more insight about battling systemic discrimination and racism (i.e. diversity hiring) than someone from a more privileged background (privileged in the sense of being from a majority group which was not the subject of systemic discrimination). Note that, like for any other hire, this type of personal experience is only one element involved in selecting the best fit for a role. I shouldn't have to say that last bit, but people like to think in black-and-white (pun intended) about race, sex, and class.
Experience is valid too. Being white or male doesn't mean you don't understand discrimination because you don't have experience with it.
An equally absurd corollary to "those that have experienced discrimination have unique insight into preventing discrimination" is "those that have experienced privilege have unique insight into privilege and how to dismantle it".
Just because you're on one side or the other doesn't make you more qualified by experience. We need people with understanding of both sides of the coin. In other words, we need diversity with respect to experiencing privilege and discrimination to understand what is happening and how to address it. When you don't have people on the other side of the coin, racist attitudes like the ones reflected in that slide proliferate.
Being white doesn't disqualify you from having experience being discriminated either. There are gay, lesbian and transgender white men, women and other gender identities. Head over to The Advocate and read some essays/blog posts from gay white males.
Furthermore, discriminating white people and men from this sphere of work (or any other) gives them some similar experiences and insight into discrimination.
What this thread shows is the sentiment that, if you claim diversity is important, leaving out a group specifically to increase diversity (as opposed to, say, merely reducing their proportion in the cohort) is in fact not being intellectually consistent or honest.
Don't fall into the flippant "Oh ho ho if white's aren't involved I guess it can't ever be legit" sarcastic dismissal. That's neither fair nor accurate.