On the other hand, the Big Bang picture does make it possible to resolve an old conflict between Ergocentric and Heliocentric Cosmologies. All the "bits of shrapnel" were once in the same place and have been flying apart ever since; in the crude approximation that their trajectories are non-interacting ( i.e. disregarding the little deflections caused by gravitational attractions between neighbours), each one is perfectly justified in regarding itself as at rest while the others are all in motion. If I am at rest now, then (in this approximation) I have been at rest all along, and am still at the centre of the Universe where the Big Bang took place, whereas all you other bits are flying off to infinity.
Even if you insist upon a geometrical definition of the "centre of the Universe," I am still at its centre, for what can we possibly mean by the geometrical centre but the point equidistant from all the most rapidly receding bits - namely, photons and other massless particles moving at the speed of light. Since these were all emitted initially from the same point where I was then, and all are moving away in every direction at the same speed (guaranteed by the STR), this is still the centre.
Of course, every other fragment is equally entitled to the same point
of view - we are all at the centre of the Universe, as viewed
in our own reference frame!