I.e., why does your brain turn off processing for the differing images to each eye cue but not for the parralax cue, etc?
But your second paragraph show's me this is all based on confusion. The parallax cue and processing different images for each eye are the same thing, not 2 different things as you're implying. And that's the one of the cues that's NOT turned off.
I'm not defending what the author is saying. I just feel you should read the article again, because your statements don't seem to address anything said in the article.
We are used to 2D: if you look around with one eye, or at very long distances: the moon, the sun and the stars are in 2D.
And we're used to 2D in drawings, paintings and photographs.
3D tries to trick you into seeing 3D by showing a different picture for each eye, but the illusion is far from perfect: according to this article we receive clues that point in different directions. And that, it claims, isn't healthy in the long run.