There is an infinity of coordinate systems that can be used to describe a roughly axisymmetric rotating body like the Earth (or practically any body in gravitational hydrostatic equilibrium). There are several in widespread use for this planet, some of which are detailed at and below
https://www.wikiwand.com/en/Geographic_coordinate_system#/Ca...When using systems of coordinates that require an arbitrary choice of origin point, one generally has to simply state what the choice is.
For the system of coordinates being discussed in this thread, the origin point is defined as the prime meridian, and it forms half of one of an infinite number of geodesics that bisect Antarctica. But because that particular geodesic is elevated to a special status by an arbitrary choice in the setting of the system of coordinates, when using that system of coordinates, it is perfectly reasonable -- under the conventions of that system -- to discuss masses that would be on one half or the other of the planet if it were divided into two parts through that geodesic.
But nobody seriously argues that the geodesic is in any way special physically compared to the infinity of others passing through the same two points (near the mean rotational poles); the Prime Meridian is a convention, and so an eastern and western hemisphere each bounded by a plane perpendicular to the meridian extended to a great circle.
Moreover, there is nothing special about this particular system of coordinates on the Earth, and the Prime Meridian does not really even have much local meaning more than a few metres away from the Greenwich Observatory, which is firmly set in what locals universally call "East London" or even "South-East London".
So, "Western Antarctica" is simply absorbing a particular choice of coordinate system on the Earth, which in turn has a defined origin point for one axis that was chosen arbitrarily. The label "Western Antarctica" is not invariant under a change of coordinates (whether by changing where there Prime Meridian is by an angle that (in radians) is not an integer factor of \pi, or by changing to a wholly different set of coordinates that use different axes altogether), and so isn't a physical feature of Antarctica, but then there's nothing physical -- in the sense of invariant under change of coordinates -- about the U.S. midwest, or Western Australia either.
However, conventional sets of coordinates on any physical system make descriptions of coordinate-invariant features easy for people who accept the convention, and understand its features and limits. (For instance, the lat-long-alt system is not very useful very close to the coordinate singularity; but that singularity vanishes under change of coordinates, and it is only a deliberate choice in matching the coordinate singularity to a point near the (approximate) line of (approximate) axisymmetry that leads to confusion like the one that appears to be gripping you when dealing with features near the coordinate singularities.)