The first mention of this kind of delusion in the works of Sigmund Freud is to be found in an 1896 paper entitled Further Remarks on the Neuro- Psychoses of Defence. Named projection by the psychoanalyst, the phenomenon cropped up repeatedly in his works over the next three decades.
Projection refers to a mental operation whereby feelings and wishes which an individual refuses to recognise in themselves - for a variety of reasons - are expelled from the self and located in another being (or thing). To escape responsibility, someone who cannot accept that they hate or love a person, envy them or want to spend the rest of their life with them, can fall into the pattern of attributing their feelings to another. So "I love you" becomes "you love me", and "I'd like to kill you" becomes "someone is trying to kill me". Entire nations can become involved in projection. In Freud's analysis, Nazi hatred of the Jews was a projection, by which the Jews were used as a repository for all that the Nazis could not face about themselves. "I fear I may be bad" became "I know you are bad".
Why is the mind prone to projection? In Freud's view, because we have so many intense wishes - aggressions, sexual impulses etc - which bubble up from the unconscious, and which are at complete variance with our conscious desires. We wish, for example, to sleep with someone of the same sex even though we are married, or we feel jealousy towards someone who is supposed to be our friend. The minds of most people, according to Freud, have only limited resources to cope with intense, conflictual feelings. The mind therefore engages a defence mechanism which sacrifices truth in an attempt to find calm. It is psychologically easier to tell yourself that it is your friend, rather than you, who is homosexual, if you have an investment in leading a heterosexual life; it is easier for the mind to decide that someone loves you than that you love them, if they are likely to reject you.
But for Freud, to be a psychologically healthy, mature individual means becoming aware of, and checking, the ever-present possibility of projection. It involves having enough mental resources to tolerate discordant, difficult emotions without off-loading them on to another person. Maturity means recognising that "I'd like some cranberry juice" does not mean "I love you".