What if all the galaxies are merely orbiting the center of the universe, but their orbit is so big that it seems like they're moving away?
The universe does not have a center.
Imagine the universe is a balloon with all the galaxies attached to the skin of the balloon. As the balloon expands each of the galaxies becomes more distanced from other galaxies.
One thing to remember though, it is believed that all galaxies a part of much larger clusters or groups. Our own galaxies is part of what is known as the "local group" with Andromeda being the only other large galaxy a member. There are about a dozen dwarf galaxies in the "local group." I mention this because Andromeda is on a collision course with the Milky Way which would seem to contradict what I said earlier.
Therefor, grouped galaxies are moving away from all other grouped galaxies according to most recent theory.