Siva is the destroyer. He is the god of death and change. Parwati is His consort. She acts his way and relieves us from sorrows.
Only after transcending death the new birth takes place. Each birth is the beginning. New birth and life begin when Ganesha is born. Ganesha is the successor of Parwati and Siva.
If it would depend on Siva, He would destroy everything and no birth would take place. So Siva is reluctant, but Parwati gives birth to Ganesha of her own.
The world carries on. This is Parwati´s mercy. If the world is no more existing, Parwati would also become idle and inactive. She would be then one with Siva.
Ganesha also has to transcend death, so Siva chops off His head.
Parwati´s heart is full of mercy, but she radiates heat of anger to melt Siva´s rigidness.
Ganesha is reborn.
A rebirth is a worldly matter, the result of desires and the outcome of Kaama. They crown ganesha with an elephant´s head, a symbol of Lingam and rebirth.
Everything has to take birth and come to existence before all activities can take place. Ganesha is first and the beginning of all. That is why we worship him first.
Ganesha is responsible for everything new that takes birth in the Cosmos. He is the symbol of fertility.
We should worship and thank Ganesha in the beginning of all we do. He is always with us if we realize each moment being born new.