Why does an aperture crop the image when you look through a lens itself but not when you look through the viewfinder?

I have been studying lenses for two days now and the aperture is very confusing. Based on the question here it appears that the aperture should not crop the image at all but when I look through a lens directly it does crop the image. When I look through the viewfinder it does not crop the image but only makes it darker as expected. Why is the image cropped when looking through a lens directly?