Analyzing power data are reported for exclusive proton-induced proton knockout from the 1s1/2 states of 10 target nuclei ranging from H2 to F19 for an incident energy of 392 MeV. Compared to free proton-proton scattering, the data are significantly suppressed, the amount of suppression increasing monotonically as a function of increasing separation energies for the knocked-out protons. It is also possible to consider that this suppression increases monotonically as a function of the increasing effective mean density for most of the target nuclei, but data for He3 and He4 targets clearly deviate from such systematic change. The data are compared to model predictions based on the nonrelativistic and relativistic distorted-wave impulse approximation. Both relativistic plane wave model and a nonrelativistic distorted-wave model incorporating a relativistic correction associated with an effective nucleon mass predict a significant suppression of the analyzing power, but the magnitude of the suppression is not sufficient to explain the experimental data. However, a relativistic distorted wave model predicts values that are closer to the data, but the result is inconclusive in this work since recoil corrections are neglected.