I just watched a really cool documentary on Amazon called Everything and Nothing. Basically it goes through the history of discovering first how big the universe is and what we generally know about it, and then how small things can get/ what is space in a vacuum.

If you learn what we know from math and scientific observations, and learn what we don't know, it gives you a good idea on why we think there is dark matter. It's essentially a place holder for observations that haven't really been explained yet.

Basically, from what we know about matter already, there are effects of only some of the Properties of matter in the universe, like gravitational lensing without any kind of black hole or star cluster or blob of gas.