>Do humans not fit the standards for being broken into multiple subspecies?
No. Multiple human subspecies did once exist (examples being Neanderthals, Denisovans, Homo Erectus, and Homo Floresiensis) but only our species, Homo Sapiens, remains (with traces of Neanderthal DNA so there was some interbreeding.) However race is a cultural and social construct. Different human races are not different human subspecies. A Pygmy, a Norwegian, a Sentinel Islander, and a Han Chinese person are all the same species. The superficial variations in average height, skin color, etc. do not vary enough to constitute species differentiation - humans share 99.9% of their DNA, and the vast majority of genetic variation exists within populations (in other words, within "races") and not between them.
Well humans and chimpanzees share almost 99% of their DNA despite being quite distant relative so that number is somewhat deceptive. Not disagreeing with the overall point of course
But the DNA of the sumatran tiger and a Siberian tiger is also over 99% identical?
> the vast majority of genetic variation exists within populations
This particular argument (I am not talking about anything else) always looked to me as "inkblot defense" (Cephalopods muddy water to defend themselves).
Genome is discrete. A single nucleotide polymorphism can have far-reaching consequences. So it's a bit like arguing that this collection of pentagons is not statistically different from this collection of hexagons because radius variation within collections is greater than between collections.
One day I've got into trouble by pointing to another genetic adaptation (EPAS1 SNPs) rather than the poster child of genetic differences: an SNP in the 6th codon of the β-globin gene. But that's another story.