Not sure if he was actually demonstrating how to throw punches in that sequence, seems like he was purposefully throwing slow arm punches for his student to block more effectively.
That was the way it was with small gloves. You blocked punches away from your head. Jackie McCoy talked about the evolution of it and explained how blocking a hook to the head was away from you, but you caught a hook to the body with your elbow. As gloves got bigger the motions became more similar. If you watch a lot of bare knuckle boxing you will see why. A lot of those dummies, with no gloves, try to shell up and cover with their hands. If they were smart about it, they would go back and watch the guys that fought way back when, like Corbett and Fitzsimmons.
It was in a book that featured several boxing trainers, written by Dave Anderson, if my memory is correct.