Why do Boys love their mothers and Girls their fathers?

 This is a characteristic of the Phallic Stage of Freud's psychosexual development.

The phallic stage is the third stage of development that occurs when the child is between 3-6 years of age. During this stage, a child’s pleasure is focused on the genitals as the child discovers that self-manipulation is enjoyable.

Oedipus Complex

According to Freud, a child at this stage fantasies about sexual pleasure with the parent of the opposite sex and tends not to prefer the parent of the same sex. Freud refers to this conflict in boys as the Oedipus complex. This takes place when a boy seeks sexual pleasure by associating with his mother but hates his father and sees him as a rival. 

Electra Complex

On the other hand, Freud referred to the feeling of sexual pleasure in girls towards their fathers as the Electra complex. It takes place when a girl seeks sexual pleasure by associating with her father but hates the mother and sees her as a rival. 

She develops a penis envy, consisting in a girl belief that she once had a penis that was just cut off. In order to compensate this feeling, a child wants to have a child with the father. A counterpart for the girl’s penis envy is the castration anxiety which comes as a fear of punishment from their father for the desire of their mother. The complexes may be resolved when a child realises that his or her same-sex parent punishes him or her for the incestuous wishes. So, a child ends up identifying with the same-sex parent in order to avoid being punished or reprimanded.