What actually causes light to diffract when encountering a slit? I've researched this and there seems to be allot of information on how light diffracts, but very little on why. The light, when closely encountering the matter in the slit is 'bent' or rather changes direction and explained as an interference between the light wave and the matter which also has wave-like properties. Is that right?
IN terms of particles, is it that the photons and matter both exert electromagnetic forces, and through these forces (and momentum exchange) the photon is diverted just like a billard ball?
Or is diffraction still a mystery in terms of why?
 A: Every finite sized beam of light spreads out as it propagates. The more confined you try to make it (e.g. a small slit), the faster it diffracts/diverges as it propagates. The reason why this occurs can be explained in a number of different, but equivalent ways: e.g. all finite solutions to Maxwell's equations diverge, light is a wave and waves diverge, there's a fundamental Heisenberg uncertainty relation between beam size at a slit and the angle at which the beam diverges.
Thinking about the problem in terms of particles doesn't buy you much, as the answer in this case is along the lines of: photons are quantum particles which act as excitations of some EM mode (which is effectively the 'wave-function' of a single photon), and this mode is the particle's wave-like part (of the particle-wave duality) and so must diffract.
A: 
The light, when closely encountering the matter in the slit is 'bent' or rather changes direction and explained as an interference between the light wave and the matter

Classically light is an electromagnetic wave;  it is simple to understand waves when seen in water, for example. The sides of the slit are a boundary that force the wave to change direction and generate interferences because of the structure of what a wave is. It is the same with water as in the video , the classical view describes  light waves too.

which also has wave-like properties.

Wave like properties of the boundaries do not affect classical water waves because the scale of a water wave and the scale of the quantum mechanical structure of the boundary slit differ a lot. 
To understand where quantum mechanics enters,  one goes to the quantum mechanical particles of light, the photons.

IN terms of particles, is it that the photons and matter both exert electromagnetic forces, and through these forces (and momentum exchange) the photon is diverted just like a billard ball?

No. Quantum mechanics describes all particle-particle or particle-field interactions with the wave function of the system under study. This is a mathematical solution of a wave equation, where the boundary conditions of the problem are introduced, the slit dimensions  width. (For the wavelengths of visible light and the width of the slits in the usual experiments, the fact that the sides of the slit are made out of molecules can be ignored). It is a "scattering of a photon on a slit width" that will define the wavefunction , which is a function similar to the classical electromagnetic wave, because it comes from the same equation transcribed quantum mechanically. The difference with the classical case is that the wave function controls the probability of the photon to exist at (x,y,z,t). The wave function itself is complex, and thus unmeasurable, but it has the sines and cosines needed for interference effects to appear. The complex conjugate square of the wave function gives the real number which is the probability of finding the photon on the screen.
The scattering of the photon on atoms/molecules , which will happen on the sides of the slit, is elastic, it just changes direction according to the probability distribution. But because of the phases in the complex psi functions, this probability is not uniform but shows interference patterns as single photons are accumulated.. The same pattern calculated for the classical beam too, because there is continuity between quantum and classical solutions.
Diffraction is well modeled mathematically, and thus understood, both classically and quantum mechanically
A: Diffraction is actually a very well understood phenomenon. So, even though physics (being a science) is more concerned with how something happens, than why it happens, I think one can to a large extent explain why light diffracts through a slit.
Imagine a beam of light that is close to being a plane wave, propagating toward the slit. At the slit part of the wave is blocked/absorbed so that only the field inside the slit remains. (The actual detail of what happens in the slit is perhaps a little more complicated, but when we consider the effects of diffraction we don't need to be too concerned about the detail.) What in effect happens is that the slit sets up a boundary condition and nature is now given the challenge to come up with a field that can exist on the other side of the slit such that it will satisfy the boundary condition. In other words, the field beyond the slit must match up exactly with the field inside the slit. Now, of course, nature always manages to pick precise the right field for this purpose, and there is always only one such field that will do the trick. 
We can compute what this field must look like with the aid of basis functions. In other words, we can use a complete set of mutually orthogonal basis functions. The plane waves turn out to be precisely such a set of complete set of mutually orthogonal basis functions. Now we form a linear combination of these plane waves by adding them with the right coefficients. We can determine what these coefficients are by imposing the boundary condition. The way we do that is to compute the overlap or inner product between the field in the slit and the part of the basis function the lies in the plane of the slit. Once we have the coefficient we can reconstruct the entire field beyond the slit simply by adding these plane waves with their correct coefficients. What we then see is the diffraction effect. (There are other methods, involving Kirchhoff integrals and so forth, but this method with the plane waves is as rigorous and easier to understand in my view.) 
In a sense what the slit has done is to create a situation where the single plane wave that was incident upon it is not enough to satisfy the boundary condition. So now the light beyond the slit needs to consist of a whole spectrum of plane waves. Their combined propagation gives rise to all the diffraction effects that we are familiar with.
Now what about the quantum way of looking at this? Well it is only after the founding fathers discovered that particles can have wave properties, described by a wave function, that they were able to explain why something like an electron can actually have diffraction effects. So it is the wave function that does the diffraction. The mathematics is exactly the same. One can again use the plane wave expansion and satisfy the boundary conditions to compute the coefficients. But the interpretation is now a little different. The wave function gives us the probability amplitude to find a photon at a particular location. One can convert this probability amplitude into a probability by computing the modulus square of the probability amplitude. Whenever we observe light, we observe the intensity, which is the modulus square of the amplitude. So then it does not matter whether we thought of this in terms of photons or in terms of a classical field. The result is the same.
