Why is there a matter-dark matter asymmetry? It is said generally that nature is symmetric. For example if light behaves as both a particle and a wave, then matter must also do so, which turns out to be true. But we find that the Universe contains far more dark matter than ordinary matter. Why? Is there a process that changed ordinary matter to dark matter?
 A: There's not reason to assume nature should treat everything symmetrically. There are many phenomena in nature that we actually know are asymmetric. For example the weak force violates parity symmetry (meaning the weak force has a preference for right or left handedness). 
A: Like it was said before, there is no a priori reason why nature should treat everything symmetrically. Much to the contrary, we know several examples of P- and CP-violating processes. And in other cases we do not even know the reason why a process is "symmetric", when in principle it would be allowed to violate CP (see: the strong CP problem).
I guess you are posing your question in analogy to the matter-antimatter asymmetry problem, i.e. that the known universe is made up of matter, while there is apparently no antimatter. However, this is a different question: we have never observed any processes that treat matter and antimatter differently. In all experiments matter particles and their corresponding antimatter partners behave exactly the same (after charge conjugation and parity inversion)
On the other hand, Dark Matter particles are very different from ordinary matter particles. A Dark Matter (DM) particle is very heavy but still stable, while heavier "normal" particles are unstable and decay quickly. This alone can already create an asymmetry between matter and Dark Matter. If you try to create DM particles, e.g. in a collider, you need extremely high energies, while it is relatively easy to create the lighter matter particles (like protons, pions, electrons, etc.)
A: Dark matter is uncharged, it might be its own antiparticle. No relationship to matter and antimatter, where mainly its charge conjugation and parity. we don't know that dark matter has any antiparticle broken symmetry. 
And there is no known relationship between matter and dark matter, except they interact gravitationally and maybe through weak interactions. 
Thus matter may in fact have enough of a CP violation that matter prevailed. Or some other mechanism. There is no equivalence to anti-dark matter, that we know of. When and if we find out what dark matter is we can worry about any of its broken symmetries. 
And no we can't create dark matter in any collider because we still don't know what they are, would not R know what it takes, we have not detected a single dark matter particle yet. We know they are there because of the bulk gravitational force. 
