I believe this is the same reason why the foreshortening effect is true, but maybe I'm wrong. The foreshortening effect is essentially things farther away become smaller.
I'm a little confused what "perspective divide" means. During lecture, Angjoo says you need to "interpolate in 3D space before perspective divide"
I'm not 100% sure, but I think the idea was that we need to do our interpolation of the texture in the 3D space accounting for perspective before taking it into the screen space, as opposed to interpolating the texture over the screen space projection of our 3D space.