Why do we measure eustatic sea-level from the center of earth?
The centre of the Earth is the only true unchanging datum.

Land masses rise and fall due to geological actions such as melting of land based ice sheets, volcanism, plate tectonics, erosion, sedimentation and ground stresses causing land masses to move relative to one another at faults.

As stated here, sea level changes resulting from,


  Eustatic change (as opposed to local change) results in an alteration to the global sea levels due to changes in either the volume of water in the world oceans or net changes in the volume of the ocean basins.


With the elevation of land altering over time (rising or falling depending on location), the true change in sea levels cannot be determined from using points on the Earth's surface as a datum; particularly when the volume of the ocean basins changes due to land mass movements.

True changes in sea levels can only be ascertained from an unchanging datum, which on Earth is the centre of the Earth.