Literally, therefore, a hypocrite was one who answers (or speaks) from under a mask, someone who is playing a part. It is easy to see how this meaning acquired a negative moral charge so as to apply to someone who assumed qualities that he did not have. He would be playing a part, only playing it in real life instead of on the stage. Whereas the real actor can take off his mask at the end of the performance, the hypocrite is stuck with it as a way of life.
The corresponding Latin word is persona, which can mean both the mask itself and the person wearing it. It is the word that gives us our word ‘person’. Its derivative, impersonate, carries the negative moral sense of ‘wrongfully representing oneself to be someone one is not’ which the word persona itself does not have.