Traditionally, men subscribe to binary thought processes, which define things in contrast to their opposites. Thus what is male is not-female, and vice versa. Because men in patriarchal cultures are in positions of relative power in comparison to females, men define themselves as active, vocal, dominant subjects, and women are cast in the passive, silent, and subservient role of objects. All the traits men find uncomfortable or unacceptable they project onto women.
Sexism is just one of the generalised forms of prejudice that projection can take.
Lacan was interested in language as the structure of the unconscious. Because the boy child has a penis and the girl child does not, she is seen by the patriarchal culture as lacking while he is seen as having. By doing this, she also allows men to feel themselves to be the objects of her Desire. Tragically, by participating in their own objectification, women are seeking subjectivity yet perpetuating the false binary meaning system which traps them as objects in the first place. Men, on the other hand, jealously guard their superior position, seeing any feminine trespass upon masculine territory as a threat to male subjectivity.