Dark matter is not THEORETICAL. There is direct evidence for it. Quoting from the relevant wiki:
The most direct observational evidence to date for dark matter is in a system known as the Bullet Cluster. In most regions of the universe, dark matter and visible material are found together, as expected because of their mutual gravitational attraction. In the Bullet Cluster, a collision between two galaxy clusters appears to have caused a separation of dark matter and baryonic matter. X-ray observations show that much of the baryonic matter (in the form of 107–108 Kelvin gas, or plasma) in the system is concentrated in the center of the system. Electromagnetic interactions between passing gas particles caused them to slow down and settle near the point of impact. However, weak gravitational lensing observations of the same system show that much of the mass resides outside of the central region of baryonic gas.
In other words, gravitational lensing of light waves - which is 100% direct evidence of matter - shows a region where there is matter that is clearly non-baryonic (i.e. does not interact with the electromagnetic field, a.k.a. "dark"). This is not subject to dispute. The question of what, exactly, is dark matter - is indeed still a subject of scientific research. There are, however, a number of super-symmetric theories which posit super-partners for well known particles, the most stable of which turn out to have the exact characteristics we're noting observationally. It is important to note that these theories were not tailored to account for the dark matter, but seem to fit the observational evidence quite well so far. As with all science however, theories are subject to falsification at any times as soon as new evidence comes on the scene.