I think the word fascist has been used so much to describe right-wing politics that the real meaning has been lost.
Yes. That was deliberate (and typical) word play straight out of the left wing playbook. It defines the political spectrum as fascist on the right and socialist on the left.
That distinction came about after Hitler broke his non-aggression pact with Stalin by attacking the Soviet Union.
Thus, if you weren't a socialist (i.e. the enlightened good guys), then you were an evil Hitleresque fascist -- you know like F.A. Hayek, Thomas Jefferson and Ronald Reagan.)
That's why I don't get into that argument. Keep your eye on the ball when arguing with leftists.