[philwelch]

You are correct that the spread of genetics and the spread of language do not have to coincide. However, in this case, it seems that they do.

If you study the genomes of the populations of Europe as well as parts of Central and South Asia, you can reconstruct a very broad family tree rooted in a shared genetic ancestry from in a population who lived somewhere in Eurasia at a certain point in time. If you also study the languages of those same populations, you can independently reconstruct a family tree of languages that culminates in the reconstructed Proto-Indo-European language that would have existed at the same point in time. The simplest explanation for this is the spread of Indo-European-speaking populations, and not merely the language itself, from a single ancestral population.