>

Native Americans out here like... uh... what about us?
But really, I think you're missing a major aspect of the science itself.

In 2003, Phase 1 of the Human Genome Project (HGP) demonstrated that humans populating the earth today are on average 99.9% identical at the DNA level, there is no genetic basis for race, and there is more genetic variation within a race than between them.

This should tell you a few things. 
1 - Race isn't genetic.
2 - Race varies far more within a racial group than it does from other racial groups.
3 - Race comes from environmental and breeding - not genetic biology.
So, with that in mind. You're talking about the .000000001% (for argument's sake) variance that exists between races as a result of their isolated histories. 
So, in that sense, you're right. We can even round it up to 1%.
So, 99% of race is a social construct. And 1% of it is genetics.
I'm not sure if that will change your view - but it should sure show you that your view is almost entirely moot.
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South Sudan and Chad are taller than the world average, and Jews and Asians are shorter than the world average.

You claimed that there are three races, but then you immediately named four, and obviously lots of people don't fit into either of these.
If the Jewish, the Asians, the South Sudanese are the three races, then which race do Scandinavians fit into? And what about the Italians? And the slavs? Which race are Tamils? Which race are native Australians? Which race are Canadian first nations? Which race are mayans? >

All Europeans, Tamils and Semitic peoples to my knowledge are all Caucasians. The origin of Australian Aboriginese is disputed because we’ve observed a phenotypic mixture between various African/asian traits… I think the best theory is that they migrated from Africa, came to asian along the way, and ended up there really long ago, and have since highly differentiated on their own. I just wouldn’t classify them as a major race, because their population and culture has dwindled massively as a result of colonialism >


All Europeans, Tamils and Semitic peoples to my knowledge are all Caucasians. 

But there are genetic differences between them... How can they be the same race? >

Not that I agree with OP, but it doesn't necessarily follow that there can't be genetic variation within the races. There can also potentially be sub-populations within races. >

But then how do we know there isn't just one race with sub-populations within it? >

That's just a matter of how we choose to define what a race is. Seems like a semantic concern to me. >

But it's a big problem for OP. He's claiming the racial categories are backed up by genetics. If we can suddenly start defining races how we want than it suggests those genetics may have ambiguity in grouping and may not actually be as straightforward as was suggested