On the site link you gave I can't see any picture that shows the crop broken off half way up the stem.

However, I have grown both wheat and barley and I have seen damage by birds where the stems are broken off well above ground. They flap their wings against the stems to bring the heads low enough to peck at. Crows (rooks) are the worst culprints and they start in any area where the crop has already been flattened by wind (or students). Pigeons usually follow the crows and peck up what they have left behind in their eagerness to flatten more crop.

It's possible that the area you refer to could be a region of bird damage extending the boundary of a student-created crop circle. Certainly the bulk of the photographs are consistent with the use of planks, ropes and rollers.

Why do people seem to prefer irrational explanations for such phenomena?

I defy anyone to show me evidence of a crop circle that could not have been created by pranksters.