What is the purpose of a single input, single output, bidirectional shift register?
a) if during left shift the output signal immediately followed the input, output changes were no longer synchronous. (And the circuit would just act as a "buffer".)
b) when you shift it left, all you're really doing is sending the data input straight to the output no:
it shifts the FFlops' data right to left, capturing Input data in the rightmost one (the one driving Output data, clocking Input data straight to the output ). All but the latest capture become observable again when you switch to shifting right and shift, only.