Frequency response based on a transfer function
simulate this circuit &ndash; Schematic created using CircuitLab

Here is a schematic of a first-order allpass.
As one can see, the phase starts at 0 deg (cap is open circuit) and goes to negative values (low pass response). For very large frequencies, the non-inv. input is grounded and we have negative unity gain (inverter) - equivalent to -180deg phase shift.

The transfer function is

H(s)=(1+R/R)/(1+sRC) -R/R;
H(s)=(1-sRC)/(1+sRC)