Fullwave rectifier theory
what concept am I missing?


If you use a rectifier bridge (four rectifiers), you don't need a center tap.  However, if you have only two rectifiers, you need a center tap otherwise there is no path for current.

Consider the following diagram



If there were no center tap, and the load were in series with the diodes, there would be (essentially) no current since one or the other diode is reverse biased during the entire cycle.