I provided an explanation for the emergence of the dark matter concept in this post, while dealing with an ignorant mythology fanboy.
As I stated in that post, the following two postulates are not particularly remarkable:
[1] the postulate that there exists missing mass - since we already have evidence in abundance for particles with mass, adding some more is parsimonious with respect to additional assumptions. It also has the benefit of being supported by simulations of galaxy rotation curves.
[2] The postulate that the missing mass consists of particles that do not interact via the electromagnetic force - again, we already have evidence for one of these, in the form of the neutrino. Postulating that other such particles exist isn’t that great a leap into the unknown as a result.
Since the particles in question possess mass, they are required to interact via gravity by definition, and their presence should therefore be detectable via appropriate gravitational effects, such as gravitational lensing. An example of mapping dark matter halos via this process, is provided here (we can safely assume that the journal Science isn’t a crackpot publication).
Any alternative to the dark matter hypothesis has to provide an explanation for data such as the aforementioned example. Without which, any alternative is dead in the water.