We don’t know actually. But what you asked constitutes the two common approaches adopted by physicists on this matter(pun intended):
First of them is that you can keep your faith in general relativity(GR), which happens to be our best theory of gravitation to date, and treat it as the correct gravitational theory then introduce a new cosmic fluid called “dark matter” with negligible pressure to the energy budget. Then you do your physics and investigate the consequences of the existence of such fluid in the universe.
The second approach is, instead of contriving stuff with a completely unknown and outlandish nature, you can choose not to trust in GR and modify it in a more flexible manner so that the modified theory accommodates features GR cannot. For example, it’s indeed conceivable the mass observed to be missing in galaxies and galaxy clusters in the context of GR are in fact a result of a far more complete theory.
Both approaches have pros and cons. However, my personal opinion is that dark matter is a strong hypothesis on many levels although we have yet to demystify its true identity. I will just leave this evidence(or need) for something like dark matter from cosmology:
(Image Source: Modern Cosmology by Scott Dodelson, Fabian Schmidt)
This is the CMB anisotropy power spectrum. Without going into details, this tells us how the density and temperature fluctuated in the early universe. Those little blue dots are obtained from the direct observation and the curves are the predictions of the ΛCDM based on the amount of cold dark matter(hence the subscript ) the model has. Notice how the diminishing amount of dark matter() causes the curves to diverge from the observed pattern. The solid black line with almost perfectly matches the reality. To me, this is a rather compelling piece of evidence.