The Rolling Stones famously sang "I can't get no satisfaction", which is a double-negative. "I can't get any satisfaction" is seen as more grammatical in modern English.
In his YouTube video, Steven Pinker said (6:13):
But "can't" and "any" is just as much of a double-negative as "can't" and "no".
I understand his broader point about one dialect being chosen over another as "the correct one", due to where the political power was, but I don't understand why "can't get any" is a double-negative.