What is the drawback of PSK and how does BPSK resolve the drawback?

You've got your terminology messed up. BPSK is specific type of PSK, i.e. PSK is the more general term with specific modes such as BPSK, DPSK, QPSK etc. being subsets of PSK. As for phase ambiguity, BPSK has that problem, i.e. in the presence of an arbitrary phase-shift introduced by the communications channel, the demodulator is unable to tell which constellation point is which. As a result, the data is often differentially encoded prior to modulation.