because they were racist. stated simply.
the nazis were operating on one of a number of competing hypothesis for the indo-european urheimat, a german word that means "homeland". after realizing that the european and indian languages derive from a common source, linguists, archaeologists and anthropologists (this was before watson & crick. there were no geneticists.) sought out to make sense of why and how that could be and try to piece together a theory about it. this is good science and all ideas should be considered, to start. it was actually an australian named gordon chile that came up with the idea that the urheimat was in germany, and a german master race of blond-haired and blue-eyed aryans migrated out of germany, across the steppes and into india, bringing european genotypes and phenotypes with them.
there's nothing inherently racist or particularly egregious about this theory. it was a decent guess based on the evidence in front of gordon chile as to how europeans and indians came to speak the same language that made sense in the era of global european colonialism. but it was one of several in existence at the time, and the fact is that we know today that it is wrong.
the theory that turned out to be correct (and proven beyond a doubt by modern genetics) was the one eventually written by marija gimbutas, that proved through careful archaeological work that the aryan urheimat was not in germany but rather in ukraine and that we can trace the spread of the aryans via their grave sites, called kurgans, from ukraine outwards in many directions - to europe, but also to china, to india, to persia, and to asia minor and south to egypt and mesopotamia. these people had horses and wagons and whether they were the absolute first people to invent the wheel or not, they certainly made good use of it to violently conquer and slaughter and replace the people around them. that's not nazism, although many ignorant people continue to think that is. that's actually well-established peer-reviewed and interdisciplinary science.
some of the initial ideas about these aryans are correct - they were gigantic, compared to settled peoples. we understand this today as a consequence not of differences in genetics but of differences in diet. humans are not pea plants like mendel might guess; we're not tall and short, and don't come out in some mix of dominance or submission. the nazis would have believed that, but that's wrong for this allele, for this phenotype. rather, height demonstrates tremendous plasticity. if we eat more then we grow more and if we eat less, or less nutritiously, then we stunt. we understand today that the aryan steppe nomads were bigger because they ate better food - more protein, wild grains - and that the settled people were smaller because agriculture had led to overpopulation, poor soil quality, less nutritious foods and deficits of protein. we have also recently learned that the nomads had much larger brains, not because they were superior and more evolved in some way, but rather because poor nutrition resulting from agriculture led to decreases in human brain sizes in settled populations, not just relatively as the bodies shrunk, but actually absolutely. agriculture and civilization really did make the settled peoples small and weak and stupid and the superior nomadic aryans really did just ride in and slaughter them all, like rats biting the heads off of house mice, or like wolves eating domesticated dogs for breakfast.
but aryan is the same word as iran. arya exists as a place name in afghanistan, but not in germany. linguists claim ireland is a false cognate with arya, but i've never been fully convinced. regardless, there are almost no traces of aryan place names in europe that we can't expain by late migration (the alans, for example, settled in france, and disappeared but left a strong trace in human and place names), but a great many place names in the east that appear to have been there for centuries.
in fact, the science states without ambiguity that these aryans, from ukraine, that spread their language and genes (r1*) throughout europe and asia, were not very european looking at all, but rather more central asian, in phenotype.
we needed the science of genetics to establish itself before we could properly understand this.
- the aryan race was indeed much larger - 6 or 7 feet tall - than settled agricultural populations, and it was warrior based, but that was not genetic, it was cultural and nutritional. they were also of a slightly darker skinned complexion (not quite olive or brown, but a beige or mixed white) than western europeans and mostly had brown eyes and black hair.
- blonde and red hair do seem to have developed in europe, but those traits were already in europe when the aryans got there. through a process of likely sexual selection (read: monster aryan men raping pretty little blond girls, many times, and over and over), the indigenous non-aryan europeans, who spoke a language with a traceable substrate but that is otherwise almost entirely lost, managed to retain that phenotypic trait, despite the aryan invasion, and not because of it. it is almost the only thing left of the indigenous european population, after the aryan invasion.
- blue eyes spread from finland in a manner that's still not fully understand, but was entirely independent of the aryan invasion into europe, and mostly just random genetic drift, aided by slight sexual selection.
this, in fact, repeated for thousands of years, until the mongols were blocked entry by a coalition of slavs and germans. the mongols were the last steppe warriors to threaten europe and no longer spoken an aryan language, but were essentially what the aryans looked and acted like.
in the end, the steppe cultures were defeated with guns and tanks. agriculture won - smaller brain sizes and all. but these periodic steppe invasions brought genetic diversity with them, which europeans needed to continue to evolve. the fact that the nordic europeans were at the end point of these aryan invasion routes likely did help europeans become a master race and conquer the world in the 17th century, but that was the end of the long war that had been happening since darius.
so, the nazis got this all backwards; the aryans, the yamnaya, were indeed very much a master race, and they did slaughter and kill and replace much of the world. however, they were not europeans in the sense we understand it; they did not have blond hair or blue eyes and were not pasty white but a kind of darker white. they were not the nordic race. the nazis believed the aryans were from germany, and used the terms nordic and aryan interchangeably, but the nordics and aryans were distinctly different groups and the aryans in truth nearly wiped the nordics out, leaving almost nothing of them but certain phenotypic traits in the places that the nodics were wiped out from. because, hey, blonde chicks are hot.
it's not entirely clear how an actual nazi from the 30s would react to any of this, if explained to them now. they had faith that the nordic race was the master race that populated the continents. the science says that's wrong - that the nordic race was a victim of the aryan expansion and not the cause of it.