The most popular version of Ardhanarishvara story of Shiva is associated with Sage Bhrigu but there is another version regarding the creation of half-man, half-woman form of Shiva. This story traces the origin of Ardhanarishvara to Goddess Parvati being jealous of Goddess Lakshmi.
Goddess Parvati grew jealous of Goddess Lakshmi because Vishnu, her husband, always carried the mark Srivastava, the symbol of Lakshmi, on his chest.
Goddess Parvati one day complained about this to Shiva and says that He neglected her. To appease Goddess Parvati, Shiva gave half of his body to her and thus became Ardhanarishwara.
The two universal parents, the father and the mother, or the heaven and the earth, are symbolized in the half-male and half-female aspects of Shiva.
The male half if Agni and the female half is Soma. Heaven is father and earth is mother Dyava Prithvi.
Heaven symbolizes the immortal world of the devas and the earth, the mortal world of matter. These are the two eternal symbols of life and matter, the duality of life and death, without either f which creation cannot go on.
Source – An article written by Harish Raja in the Tattvaloka February /March 1993 issue.