Why is the possibility of the universe having a centre around which everything orbits not considered feasible? I'm sure there is some kind of reason as to why this isn't considered as a legitimate theory but upon giving it though it seemed to make sense to me. I figure if all gravitational orbits are essentially spiralling in to the thing they are orbiting then the closer a galaxy is to the centre the faster it moves to this centre, explaining red shift. This would also explain blue shift of certain galaxies assuming they are further from the centre than we are. I have read articles about how the universe apparently doesn't have a centre thus disproving this but I find this hard to comprehend and accept, if nothing else I would appreciate if someone could explain this concept to me.  
 A: Because when we look around, we see that things are, on large scales, the same in all directions.  This would be true in such a model only if we were at the centre of this system.  That seems ludicrously unlikely: what are the chances that we are lucky enough to be at the one place in the universe where everything looks the same in all directions?  So instead we assume that our position is nothing special, and that the universe looks the same on large scales wherever you happen to be.  This immediately rules out such a model.
(More sophisticated observation of the large-scale dynamics of the universe also rules out such a model, but this assumption of non-specialness of our location is an important principle, I think.)
A: Our universe looks not only isotropic (the same in all directions) but also homogeneous (the same at each x, y, z at any one time). The fact that our position is not unique is not a principle, it is determined to be so from astrophysical and cosmological observations. Of course, the meaning is that these are so for cosmological distances, i.e., in the large, for instance at distances of 100 Mpsec or more; local inhomogeneities or anisotropic so like solar systems and galaxies or Galaxy clusters need to be averaged over those longer distances to see the homogeneity and isotropy in the large. Seeing in different directions we can do directly. For homogeneity it is a little indirectly (more sophisticated in @tfb's words, as I interpret it), in that what we see from here, or what we'd see from a typical Galaxy 1 billion light years away, looks the same, only different because the other Galaxy is a billion years younger, so we have to adjust. 
If you assume homogeneity and isotropy for the universe, you get the Friedman-Lamaitre-Robertson-Walker cosmological models, which expand the spatial part of spacetime, and only have the 3 possible spatial geometries (positive, zero, or negative curvatures). All 3 expand, but one keep on expanding faster, one slows down, and one just goes on going just barely. They are called open, closed and flat universes. In all those cases there is no center, no special place, and all galaxies see the same redshifts for galaxies at equivalent distances, i.e., they all see the same expansion, only scaled by how old they are (the further away we see the younger the galaxies, in the large.
The cosmological model that best matches the numbers on expansion and so on, and also the measurements of the microwave black body background, is called the Lambda-CDM model. You've seen it probably already, where that includes the dark energy (lambda), cold dark matter, and tHe observable mass and energy of the universe, and at this point the numbers favor a flat (spatial sections) universe. 
It is hard to visualize, but plenty of those online you can try. In all cases you see that no single point is unique.
Also by the way, again that homogeneity and isotropy is not a principle, it is 'observed' in the way explained. That has led to a theory as to why out of what might have been a very random beginning after the Big Bang things could get to look so uniform. The theory is called Inflation, or the Inflationary universe. That might explain it, it is the best we have, but there still could be some other explanation. There's data to support it but not exactly a full confirmation. There some gravitational radiation that would be explained by it, and people are looking, but not yet detected (the black hole gravitational waves detected have a different source. Need bigger detectors for the Inflation-sourced gravitational waves. There's otherthing they are looking for also. But if found, that would actually explain why we are so homogeneous and isotropic. 
