In the image you posted the transform pivot point is definitely set to the 3D cursor. It’s possible that in a previous lesson he had you change it for some reason. Sorry, I haven’t done that tutorial but possibly he had you copy and rotate the fins around the 3D cursor? At any rate, the transform pivot point is definitely off somehow.
If you chose “Median Point” from the dropdown and it disabled rotating and scaling I’m not sure what the issue could be. I’d have to look at the actual blend file if you want to share it.