But the question is why not. If the filioque is necessary to defend the Son’s divinity why wouldn’t the Spirit need to beget the Son in order to defend the Spirit’s divinity?
That is a subject that can be dealt with outside of the filioque and the Creed. Because you call into question the Spirit’s divinity, when the filioque never does.
One reason is to falsely teach; “the Spirit need to beget the Son”, I think the locals and the bishops in Spain would of put the Pope in a white jacket and called a mental doctor.
I don’t think it was necessarily just the divinity of Jesus Christ, but when Jesus attained His divinity was also infecting the Creed at the time.
This subject relates to the historical present situation of the heretics who are teaching the flock that Jesus is not God but became God at a later time.
For one illiteracy is very high among the fold, so a major theological discourse of the divine eternal procession and divine essence by the Pope or local bishop is not profitable.
Yet, because the fold are aware of the Nicene Creed which everyone professes and the heretics are infecting the source from which they teach their heretical views. The filioque quickly extinguished the heretics teachings. When the heretics have no authority on the matter when it came to what is professed in the Liturgy.
The faithful never doubt the divinity of Jesus Christ, until their heretical teachers or wolves entered the fold teaching heresy from what is already believed from the Nicene Creed. The Pope in order to remove the heretical infection, included the filioque without spilling blood, and protected the Apostolic faith which professed that Jesus is God incarnate, and there never was a time that Jesus was not God.
We have to remember the filioque is not something new by 1014 a.d. The theological understanding of the filioque already exists among the Magisterium.
It is the Nicene Creed and the faithful who need to be protected and tended by Peter, not a theological discourse to defend what would of given voice to known heretics, but to remove the wolves (threat) from the faithful.
The filioque when professed with in the Creed limits the filioque only to what is professed within the Creed. Which removed the heretics and exposed them before the faithful, when it is professed without doubt Jesus is God because the Holy Spirit proceeds from the Father and the Son.
When the Arians infected the East, the Church developed the Nicene Creed. I would ask, why did the East develop a new creed, when we already had the Apostles Creed? To answer this, would answer your question why, the Pope included the filioque to defend Jesus is God incarnate.