Requirement of center tap in PoE applications
Here is a schematic diagram of the ethernet magnetics.

The DC current flows from the PoE injector into the center tap where it splits.

Half of the current flows through the transformer winding in one direction, and the other 1/2 of the current flows in the opposite direction, thereby no net magnetic field is created by any changes in the DC current.

No net magnetic field means that no signal is injected into the ethernet data stream. 

Similar thing happens at the other end.

from: avnet.com