Shiva Parvati got Ganesh as their Son, by thegrace of Vishnu

The Maha Bhagavata Purana states the Vishnu himself is Ganesha. The story goes that when Vishnu saw Kartikeya cuddling in the lap of Parvati, he desired to experience the bliss of being the son of Jagadamba and drink her nectar milk. The Goddess sensed this desire of Vishnu and granted him the boon that he'll surely become her son. Thus, the Goddess gave birth to Ganesha who was none other than Sri Hari himself. She embraced him and made him drink her milk.

After Shiva had beheaded Ganesha, he apologized to Vishnu that just as he has beheaded him in the form of Ganesha, a time will come when Vishnu will incarnate as Sri Krishna. As Krishna, he'll come to battle with Shiva in Shonitpura, and there, the weapon of Krishna will benumb Shiva so that he'll be unable to further fight in the battle. He will equate himself with Vishnu in knowledge, culture, wisdom, prowess.this is the reason why Ganesh is 2nd most intelligent being after Mahavishnu.

On the face of it, this story seems to make our gods finite: Shiva is not omniscient here, neither is Ganesha and Mother Parvati is distraught. The other Gods and Goddesses also participate in a war and lose to Ganesha. Truly, this story seem to suggest that all our omniscient, omnipotent and omnipresent gods behave in a very human manner!! But at a deeper level this story is symbolic.

Ganesha was created by Parvati without Shiva. Ganesha obstructed Shiva from entering his own house. Shiva beheaded him and replaced his head with an elephant's head. In this story Parvati is the universe and Shiva is its God, and the son of Parvati is us. Any creation of the universe that behaves without the God's sanction/approval cannot exist for long. Ganesha was obstructing the God from the universe. [that is , he was behaving in a manner that showed his utter ignorance and disregard for God] Such a behavior is not acceptable.

Shiva beheads Shri Ganesh. Head is the seat of all Ego. Shiva destroys it to remove all Ego. Shiva replaces it with an elephant's head. An elephant is symbolic of being a non-violent, strong and wise animal. So in that way Shiva destroys the Ego and replaces it with wisdom. Ganesha becomes the leader of the Ganas. Those of us who become devoid of ego naturally become leaders since people now respect our wisdom. Shiva is called as Ganesha's Father. This shows that in ignorance we may behave in a manner contrary to God, but God removes our Ego and makes us wise. God shows us the way like a father.

Ganesha is to be remembered as the remover of obstacles and be invoked before all undertakings. Our wisdom should be used to plan ahead and remove our obstacles, and a review of our plans before any undertaking shall decrease our obstacles and problems in the future and ensure its success. Please note, this is the interpretation that makes the maximum sense to me and no disrespect is intended to any deity.

We all recognize that Parvati was ready to destroy the world in order to restore Ganesha and also that Shiva accepted Ganesha as his son in spite of all the drama. We all subconsciously hope that She and He will show us the same mercy when we make mistakes. This is also why we all feel a close/comfortable relation with Ganesha, as if he were our older brother. Jay Shri Ganesh