Why does light behave like a wave? When discussing a single or double slit experiment, where light is shined through a very small slit, it is often compared to a water wave going through a similar, if larger, slit. It's my understanding that when a ripple hits a wall with a hole in it the reason the ripple "bends" and spreads out is because of internal attraction between the water molecules, which are polar. So the molecules on the far side of the slit with energy will pull on the ones without and create a diffraction pattern; and I believe that a similar argument could be made for sound waves, that the molecules the wave travels through are at least slightly polar, or at least they have mass and momentum, so they will push/pull each other and create a diffraction pattern . But as far as I know light exhibits none of these properties, So what property of light allows it to diffract? Shouldn't light which passes through the slit be completely unaffected by the light which hits the material?
Clearly light sometimes behaves like a physical wave; but I was wondering if this physical behavior can be explained with some intrinsic property of light. Similar to how a wave travelling through a physical medium can be explained with different attractive forces and momentum.
 A: Your question is a fantastic one!  It shows that you are inquisitive and unwilling to take a book's word for it.
To address your question, we could just as well ask the question like this:

In order for a wave to propagate, there either has to be some
  restoring force, or there has to be a way for one "unit" of the wave
  to push or pull on the next unit of the wave.  What force or
  phenomenon allows one "unit" of an electromagnetic wave to pull or
  push on the next "unit" of the wave such that an E/M wave can
  propagate through space, and do all of those "wave things" like diffraction?

The answer to this is that:
a.) a changing electric field gives rise to a magnetic field.
b.) a changing magnetic field give rise to an electric field.
Each of these, acting in turn, is an electromagnetic wave.  Oscillating "units" of the e/m wave give rise to other oscillating units of the wave through electromagnetic induction.  All wave behavior, including refraction and diffraction, follow from this.
A: For the water waves the restoring force is gravity, and there is a circular symmetry for any bump.
For sound, it is a pressure wave, and there is a spherical symmetry for a region with higher or lower pressure and the surroundings.
In both cases, it would be strange if they follow a straight line after the slit, without spreading.
The behaviour of light depends on the size of the slit compared to its wave lenght. 
A: Yes water and sound waves are share similarities but are also very different to light waves which travel in a vacuum. Diffraction of light is caused by an interaction of the EM field of the photon with the EM field of the material at/in the slit edges. Any size aperture will effect the light path to some degree. The light path bends showing the diffraction. ( "Interference" though is the result of another phenomenon, the wave property of light that requires it to travel n multiples of its wavelength.)
Your question highlights that light waves/particles propagate independently as compared to matter molecules that can push/pull on each other. 
A: In physical waves as you correctly pointed out, there’s an interplay between inertia and a restoring force, exchange and balance between kinetic energy and potential energy. 
Analogously in case of light as @the_photon has already pointed out, there is an interplay and balance between electric and magnetic field which is beautifully captured by the Maxwell’s equations. In a loose sense, the electric field “pulls” on the magnetic field which in turn “pulls” on the electric field in a cycle. In fact this is the reason why light, an electromagnet field doesn’t need a medium to travel in as the fields are self-sustaining. The fields themselves are the medium!
