With a transformer center tap, why are the two resulting circuits out of phase by 180*?
If you had two 9 volt batteries wired in series to produce 18 volts you could connect the lower battery negative to ground and you would have ground aka 0V and +18 volts.

If, instead, you connected the centre tap of the two batteries to ground you'd have -9 volts, 0V and +9 volts - the +9 volts is, in effect, 180 degrees different to the -9 volts.

So, a centre tap on a transformer does the same - if you reference all voltages to the centre tap (let's call it 0V) then one end of the winding would reach maximum positive when the other end of the winding was reaching maximum negative.