It's sociology, they can't tell you the reason why because they don't know. Instead they rely on people wanting it to be true, so they build a "common sense" argument that lacks evidence.

When these people push for diversity they often mean "have every skin tone represented in your team photos". While this feels nice and would certainly repel any accusations of not being "diverse enough" it is the wrong kind of diversity. Now here is my "common sense" argument:

What people actually want is a diversity of opinions. This you can imagine having a positive effect on performance as each member of a team would have a slightly different take on things that may allow the group to discover a better solution. This would explain why the diversity of skin tone type approach somewhat works, as different races usually have different experiences, which usually means more diversity of thought when compared to a completely homogeneous group.

The obvious drawback to diversity of thought is that it's harder to quantify and optimize for. Anyone can look at a team photo and tell if a race is over/underrepresented because we have evolved incredibly advanced pattern recognition abilities. You can't easily tell what someone's opinions are without talking to them for a little while. Management already has trouble hiring qualified candidates since they don't know what qualified candidates look like, so adding diverse thinking to the list of criteria just exacerbates the hiring problem. Plus if you actually could select thought diverse candidates you run the risk of not including all races, opening yourself up to accusations of bias that can be devastating in today's politically charged climate.

Social science can't accurately model single humans well, let alone groups of humans as they attempt to solve problems. Even my analysis that we really ought to be concerned with diversity of thought is based on intuition rather than experimentation. It's a hard problem domain, and the solutions may not be intuitive.