The gravitational lensing evidence suggests the existence of massive and relatively dense regions of dark matter. However, if dark matter interacts only gravitationally, what would stop it from collapsing to a black hole of any size? For example, if there is a cloud of a dark matter gas of the mass of the Moon, and this cloud over time condenses under its own gravity down to the size of the Moon, then what would hold this object from quickly collapsing to a singularity with no electroweak of strong force to resist the collapse? Would the Pauli exclusion principle apply to dark matter to create a degeneracy pressure preventing the collapse?
Conservation of energy. If a cloud of normal matter collapses then it loses gravitational potential energy. Various processes then ensure that only (roughly half if the virial theorem applies, for quasi-static collapse) some of this energy is thermalised and become kinetic energy of the particles, whilst half is radiated away.
This can't happen for dark matter. The same dissipative processes do not occur, it can't radiate away energy, and the dark matter would pick up exactly the same amount of kinetic energy that would enable it to expand again.