Why do waves, specifically light, diffract through a slit?

A plane wave, by construction, has all frequency components in the direction perpendicular to propagation. Now you let that impinge on a slit (or multiple slits) - you are now altering those frequency components, and what comes through the slit(s) is no longer a plane wave but the Fourier transform of the real space slits.

Now, the link to Huygen is pretty straightforward - it is all related to the surviving frequency components between the plane wave (a solid line of the wave sources) and what comes through. The math is all the same.

Light diffracts primarily because there is an interaction of the EM field of the aperture material with the EM field of the photon or wave. Diffraction is interesting in itself but it is also the diffraction pattern or "interference" pattern that results which causes a lot of discussion. The word "interference" is historical but also somewhat misleading, 2 photons never "interfere" or cancel, that would be a violation of energy conservation, instead photons take paths that are of certain pathlengths that are integer multiples of its wavelength ... this can explain the "interference" pattern. Mathematically this coincides with the use of Huygens principle in double slit experiments.

For water or air you could have the movement of 1 molecule radiate outwards and effect many other molecules in a circular pattern. Light is different, a quanta will radiate in one direction only.