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I am not aware of any official Church teaching on the matter but the following is a Catholic opinion.
Some people might mistakenly believe that God and Satan are some type of rivals or even equals, however, Satan is merely a created being, infinitely less powerful than God.
God did not defeat Satan Himself primarily because it would not be fitting for him to even acknowledge Satan as worthy of being personally attended to. Just as a mighty Emperor sends his soldiers to quench a petty insurrection so the Almighty sends his angelic army to destroy the forces of evil.
The fact that St. Michael the Archangel was of lower rank emphasizes the humiliation of Satan who used to be the most brilliant of creation.
There are also other considerations that might have prompted God to use St. Michael in this way, such as providing us with an exemplary intercessor for our prayers and shield against evil.
We must not also forget that St. Michael is also a being whose good God desires and, seeing him worthy, he judged it fitting to reward him and exalt him for his humility and courage.
This exaltation in no way diminishes the glory of God since St. Michael in his humility gave himself up to be a mere tool of the Divine Will.
Let us ask for protection from the snares of the Devil by praying the prophetic prayer to St. Michael the Archangel given to Pope Leo XIII which predicted the present apostasy in Rome:
These most crafty enemies have filled and inebriated with gall and bitterness the Church, the spouse of the immaculate Lamb, and have laid impious hands on her most sacred possessions. In the Holy Place itself, where has been set up the See of the most holy Peter and the Chair of Truth for the light of the world, they have raised the throne of their abominable impiety, with the iniquitous design that when the Pastor has been struck, the sheep may be scattered.
I hope my answer was helpful!