These depressions in space (gravity wells) express the classical understanding of gravitation (Relativistic, not Newtonian), which suggests that gravity is not a measure of the force of attraction between two bodies, it is instead a measure of the force with which two bodies fall into the larger gravity well produced by the overlapping of their two individual gravity wells. This means that we could essentially describe the riddle of Dark Matter in another way, by simply saying that we cannot explain how the gravity depressions in which galaxies exist can be deep enough to prevent the spinning matter within them from over-spilling their boundaries.
So, before tackling the question of how these depressions can exist at all, we should first ask an even more basic question. If we concede that such depressions do exist, then perhaps we can first attempt to understand whether the matter within galaxies behaves according to our understanding of gravitation. In other words, start with the simple acknowledgment that sufficient gravity must be present within these galaxies for them to hold their shapes, even though we do not know why or how. Once we have made this leap, we can then ask ourselves whether the behavior of these galaxies then falls in line with the predictions of Gravitation.
Fortunately, the answer to this question appears to be a rather straightforward, yes. Indications are that once we acknowledge that there is indeed sufficient gravity to hold galaxies together, meaning the gravity wells they are in are in fact, deep enough to contain them, some of the mysteries that have given rise to the theories of Dark Matter already begin to dissipate. Once we clear this hurtle, galaxy rotation and structure is no longer mysterious; we are left only with the need to explain why these wells are deeper than it seems they should be.
The very acknowledgment that gravity wells exist is also acknowledgment that spacetime can bend. Space is far from empty. Hubble's Law postulates the notion of structured Spacetime as the expanding agent upon which matter is resting. And, as we have seen, General Relativity describes gravitation as the curvature of spacetime caused by the presence of mass. This means that the next leap we must take is to begin considering whether spacetime is always flat in the absence of mass. Is matter the only thing that can bend it?
As we continue deconstructing the problem of Dark Matter we find that one of the underlying premises upon which it is based is the assumption that only matter can bend spacetime; that in the absence of matter, spacetime is always perfectly flat. But we must ask, is this a well-founded assumption or an accidental one? If we concede the possibility that the spacetime fabric, which we know to be bendable by matter, could possibly bend for other reasons, then we have already begun to dismantle the need for Dark Matter.
From here we can view the entire problem of galactic structure in terms of that curvature. The only remaining question is what other influences could be bending space? Why are galactic gravity wells so deep?