Dark matter can explain: the large scale evolution of the universe (together with dark energy but whatever), rotational velocities of galaxies, gravitational lensing and other phenomena. No other theory explains all of these things as well or simply.

Also, dark matter is not really so exotic and weird. We already know of one type of dark matter particle, neutrinos. To think that there are other more massive particles that only interact through gravity and the weak force isn't much of a strectch in that light.