Your professor is right in a sense: you can’t blow up digital work and expect a sharper image. A little math: Each image is just a grid of colored pixels. When a computer makes a picture 2 times as big, 1 pixel becomes 4 pixels. The computer then guesses what color to fill in those 3 new pixels, and sometimes it makes pretty bad guesses.
However, there are plenty of ways to avoid that effect. Mostly just draw at the resolution you want to print (I work at 300ppi). The computer is better at guessing pixel color when downsizing (averaging 4 pixels down to 1). However, this makes for huge files (especially when you multiply by the number of layers).
We don’t all have supercomputers. What I’ve discovered is, when printing, you can get away with up to half the dpi (150 ppi). Printers work by squirting dots of ink on paper, and these dots are often bigger than screen pixels. So whether you work at 200ppi or 300ppi, there’s not much difference because the ink dots can’t get any smaller. What you are printing on can also affect your lowest dpi: rougher, more absorbent papers or canvas will let you get away with a lower dpi because the ink dots will naturally bleed no matter what.
Personally, I’d say your professor is being “stupid" to say SAI and PS are "stupid." What’s "smart" is to know the limitations and capabilities of your materials - whether digital or traditional!