Why isn't the universe travelling at $c/2$ to the left? Consider two inertial observers starting from the same spacetime point, one remaining at rest relative to the CMB and one moving at speed $c/2$.
According to relativity theory, neither observer has a preferred status - no local experiment would allow you to determine your velocity in an absolute sense.
However the first observer has a preferred status in that he observes the universe as approximately homogeneous and isotropic whilst the second does not.
This situation is often described by saying general relativity is a background independent theory but the background is determined 'dynamically'.
What is this dynamic mechanism which resulted in the first observer having this preferred status? I am just trying to get a handle on whether this is a meaningful question to ask within the current state of mainsteam physics or not. I will accept a simple "No" as an answer, but any justification would be appreciated.
Edit: I am not asking if the existence of a preferred frame contradicts relativity, but rather whether this situation points to a deeper more natural theory of spacetime where we don't have to just say "this is the universe we find ourselves in".
Edit: The two given answers has allowed me to give a more precise statement of this question: "Of the 10 Poincare group degrees of freedom, our universe appears not to have a preferred spatial origin (3, homogeneity) , not to have a preferred spatial direction (3, isotropy) but it does have a preferred temporal origin (1) and a preferred (local) Lorentz boost (3). Can we explain the latter of these?"
 A: Maybe it's easier to work by analogy with a simpler example.
The laws of physics are invariant under rotations in three dimensions. But you certainly do not experience "up" to be equivalent to "north" and "east," because the Earth's gravity pulls you down. Is there a contradiction? No -- the fundamental laws are invariant, but we live on a planet, and the effective laws we experience on this planet are not invariant under rotations that exchange "east" and "up" (for example).
It's really the same situation in cosmology. The underlying laws are invariant under Lorentz transformations. But the initial conditions of the Universe had a frame at which the matter was (on average) at rest, and so the specific Universe we find ourselves in has a preferred frame.
A: The "preferred reference frame" thing is really about flat spacetime. When ignored, it leads to statements such as "You can't go faster than light because your mass increases with speed, diverging at $c$" ["You can't go faster than light because at any speed, you're still rest in your frame, and light moves at $c$ in all directions", is better].
Also: "Time slows down for a twin on a spaceship". [In the twin paradox, each twin sees the other's clock ticking slower].
Enter GR and cosmology, at any point, one can define a preferred rest frame that is (roughly) at rest with respect to the CMB. The problem with this as "defining a preferred frame" is that it is local. Every point in the universe has a different velocity (hence: the Hubble constant).
If every galaxy we see had a zero peculiar velocity (including the Milky Way), they would all be "at rest" relative to the CMB, but each would have a velocity relative to the other.
In your example, with one observer moving at $c/2$, if he were suitably far away, then both observers could be at rest relative to the CMB.
