Think about a ball and that you slowly blow air into it. From any point on the surface, it seems that everything is going away from that point. And there is no specific center on the surface of a ball.
It shouldn't be hard to visualize that in 3D even without the warping.
As for the red shift: the reason is simple, yet I wasn't able to get a good explanation of it apart from the usual sound analogy bullshit.