Of course a given gene comes from either parent. But... Every new child is a new combination of DNA. Just because a particular gene comes from either the mother or the father does not mean that it can be traced back through ancestral lines... You are saying that we could, in effect, work our way back through all of those shuffled and recombined decks.
If you mean determining what combinations of genes which ancestors had so each past individual's entire genome is completely known, of course not, and nobody's taken a position requiring that. If you mean studying one chunk of DNA and its history on its own regardless of what other chunks are also present with it, then of course that can be done, and routinely is. You seem to have no trouble accepting two examples of it yourself: mitochondria and Y chromosomes. But it's precisely the same with a gene on a non-Y nuclear chromosome. Whatever single chunk of DNA you look at, whether it's a Y chromosome or a mitochondrial genome or a gene from some other nuclear chromosome, it always ends up in new combinations with the others in every generation. If the fact that a given Y chromosome ends up together with a different mitochondrial genome and a different set of other nuclear genes in each generation doesn't disrupt Y chromosome studies, and the fact that mitochondrial DNA ends up together with a different nuclear genome in each generation doesn't disrupt mitochondrial studies, then why would the fact that any given gene in a non-Y nuclear chromosome ends up combined with other genes in each generation be a problem for studies of that individual gene? You originally said that recombination would "erase" that line, but how would it do so, and why have the geneticists who have done exactly that kind of work on individual genes not noticed whatever this mysterious problem is?
And most of all, what would that even have to do with the subject here anyway, since the fact that human races are human races does not depend on either of the two things we're talking about here (separate inheritance "lines" for single genes, or knowing the entire exact genome of all of an individual's ancestors)?
So now not only do you need a grouping below the rank of sub-species
I don't, because I don't subscribe to the utter silliness of claiming that an entire living species is all just a subspecies simply because it had ancestors who weren't quite the same. By that standard there could never possibly be any such thing as a living species whose present population isn't "just a subspecies", which is why it's not used for any other species. But it's a pointless, meaningless little trifle which has no effect on the subject here anyway, so I'll play along

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you even need to break each of these up into further sub-groupings.
Why not? What's wrong with that? If a population splits, and then at least one of the resulting populations splits again, and then at least one of that new set of populations splits again... why would anybody want to dictate how many times it's allowed to happen instead of just acknowledging the fact that it did happen whenever the evidence says it happened?
Delvo, people are not denying race exists. We are saying they are not true biological divisions.
Those two sentences directly contradict each other. And the first one is directly contradicted by a lot of the posts in this thread.
It is a social construct because one choses where to draw the lines, rather than the lines existing because of natural separation of the groups.
You you're back to lying about the nature of the known clusters of traits (both phenotypic and genetic) and what correlation is.
In biology, subspecies need to be genetically isolated.
That's "species" you're talking about there. Who has claimed that the human races are different species?