Projection is a natural thing that many, no all of us do from time to time. It has also been identified by Freud as a defence mechanism. A defence mechanism is a psychological process employed by a person to save them from anxiety and one could say to save their self image as a good person.
For example a peace protester may have significant aggressive impulses inside him. He is disturbed by these impulse so they cause him anxiety and they do not fit with his own self image of what a good person is.
As a consequence his unconscious takes over and solves his anxiety. It gets him to project his aggressive impulses outside onto someone else or perhaps some organisation. This allows him to avoid his anxiety and maintain a good self image because in his conscious mind he has no aggressive impulses. Due to his non aggressive sense of self he becomes a pacifist and goes on peace protests, (Also because he is unconsciously frightened of his own aggression).
He sees the government as being very aggressive at least in part because he has projected his aggressive impulses out onto it.
Hence we have
“The lady doth protest too much, methinks”.
William Shakespeare (Hamlet)
And the icing on the cake comes when he can go on a peace protest and express his aggression towards the police (who he has also projected his aggressive impulses onto). This aggression does not cause him anxiety because in his mind he is being aggressive in the quest to achieve peace.