Or it was elites and invaders that spoke Aramaic and Greek, while the peasantry, who never had a reason to abandon it, still spoke Hebrew.
The Mishnah, which included records of debates from at least a generation or two after the destruction of the Temple, was composed in classical Hebrew. The generations that followed apparently had their discussions in Aramaic.
I don’t know if the elites would lose a language ability they once had since it was the elite who controlled the rituals and needed the language. But, who knows...?