How did the Anatolia hypothesis explain the spread of Indo-European languages into Europe?

The Anatolia hypothesis, most notably championed by archaeologist Colin Renfrew, proposes that the Proto-Indo-European homeland was located in Neolithic Anatolia during the 7th millennium BCE.12

According to this theory, the spread of Indo-European languages into Europe occurred alongside the expansion of the Neolithic package, which introduced agriculture to the region. Proponents argue that as early farmers migrated from Anatolia, they carried their language with them, facilitating its gradual dispersal across the continent.123

This hypothesis stands in contrast to the more widely accepted Pontic-Caspian steppe theory, which suggests a later expansion during the Bronze Age involving nomadic populations. Critics of the Anatolia hypothesis note that the spread of farming was not a uniform process achieved solely through population migration, and some linguists find the theory difficult to reconcile with established linguistic evidence.1234