It absolutely does mean that group A is being given more opportunities than group B when you realize there is no difference biologically between group A and group B.
Yes, in a world where those two groups have the exact same make up, it would mean that. That's not true at all in this context. There are differences between racial groups. No one is shocked and appalled that Jewish people are hugely over represented as Nobel prize winners, or that black people are wildly over represented in professional sports. It's difficult to disentangle what is just cultural impact, but they're patterns that a child could identify.
If you work from a false premise, you end up with false results. The motivation behind the desire to believe that everyone is equally capable at everything is a good one, and individuals should be treated as if they have equal potential regardless of their immutable characteristics. It would be great if all groups were great at everything. If it were possible, I would make it so. However, falling prey to treating "ought" as "is" leads to pathological behaviors, which is exactly what is happening to the well-intentioned members of this movement.
This is not true, genetically, and if you believe there is, that's a real problem for you.
As for the differences in these communities as a result of differing treatment by others, you're damn right there are differences, and to the degree that those differences are caused by discrimination and hatred (and it's a high degree), that's exactly what we're trying to slowly improve.
The problem with your egalitarian vision is that not everyone starts out on the same level, and if you ignore the systemic ways people are held back, you ruin any shot you might have at getting the end goal you seem to want, which seems to be "may the best person win".
We all want that end result, but until you deal with reality, that's never going to happen.
And why do those cultural differences exist? What bonds "black people" together in American culture, despite coming from a whole host of diverse places that otherwise share little to no culture amongst one another?
