gravity - Why dark matter and general relativity?

My knowledge on this subject is minimal, so sorry if my question is obvious. But why is the current consensus that there is something called dark matter rather than that our current theory of gravity (general relativity) is wrong?

Edit/comment

The answers so far have given evidence for dark matter and general relativity. But (this may seem like a bit of strange thought) are we not doing the same as we did with the aether and the aether drag hypothesis? I.e. there is an observation that does not fit with general relativity what we are doing is assuming that general relativity is right and designing 'add on' theories [i.e. dark matter] to make all other observations fit GR. It seems to me that we are just holding onto general relativity because we are 'use to it'. It is like the saying we are 'looking for life as we know it', who says life can't be something completely different (rhetorical question)? This also goes back to Occam's razor, dark matter cannot be explained without making the whole thing more complicated. Another theory of gravity seems like the most simple approach.

Answer

Because General Relativity has an overwhelming amount of experimental evidence to support it. As a result, physicists look for dark matter, which works within GR, rather than to throw the baby out with the bath water, and thereby assume GR is wrong.

When Albert Einstein introduced the world to GR, he proposed three tests that would support GR. Please keep in mind that at the time, these predictions (except #1 below) had not been previously observed, nor could they have been explained with any previously existing physical theories.

1. Perihelion Precession of Mercury- Basically, the precession of Mercury's orbit could not be explained by Newtonian gravity or Kepler's Laws of Motion. In fact, people were so hard-pressed to explain this precession that one hypothesis even suggested a previously unobserved planet orbiting between Mercury and the Sun. However, after Einstein developed GR, he showed that the part of Mercury's precession unexplained by other factors could be attributed to the curvature of space-time.


2. Deflection of Light by the Sun- Einstein proposed that light could be deflected by gravity, due to GR. This was observed in 1919 during a solar eclipse, when the position of stars "near" the sun (I use "near" in regards to their apparent location on the sky's dome, not "near" in space) was shifted slightly, due to the Sun's gravity. Although the original experiment has been criticized, this effect has been reproduced many times since it was originally observed.


3. Gravitational Red-Shift of Light- In 1959 the Pound-Rebka experiment observed a relative red-shift of light between two different light sources, due to gravitational effects of the Earth.

Each of those tests has individual Wikipedia pages, linked to under the first link I included above. Additionally, there are a number of more modern tests of GR, not limited to just the three I described above.