It is not in what the theory explains. It is in the fundamental assumption the theory is based on. MOND demands the Newtonian dynamics to be modified in the large scale universe. However, Newtonian mechanics has been proven to be correct from the microscopic atomic scale to the macroscopic scale of the solar system. There is no compelling reason it should not work and need to be modified in the large scale universe since it has never been proven to be incorrect in any other branches of physics. And the assumption doesn’t seem to shed any new lights on any other major cosmological problems.
Furthermore, the problem is not only in their assumption, but also in the missed understanding of the additional long range gravity force that has been eluding the physics community for a long time. Typically known as the tidal gravity force is a conceptually misunderstood force that has never been mathematically formalized but thought to exist if the equivalence principle is assumed to be correct on which general relativity is fundamentally based.
The fact that Lens-Thirring force could be derived from dipole gravity force indicates that Lens-Thirring, tidal gravity, the gravito-magnetic forces are fundamentally the many different manifestations of the same dipole gravity force resulting from the rotation of a longitudinal axially asymmetric object like a cone or a hemisphere due to the component wise accumulation of the acceleration induced gravity force.
A theory starting with a totally unjustified assumption and with the missed long range gravity force can not be correct even if it may explain anomalous galactic rotation curves.
The more serious problem with the theory may be on what it doesn’t explain. The jets from the black hole accretion discs and the planet Saturn mystery seem to have nothing to do with MOND.
Of course, one can always argue that MOND was not meant to explain the jets nor the planet Saturn mystery but obviously that's a self defeating argument because dipole gravity was not even meant to explain anything other than finding its own place in general relativity.