The name is in the title so ill get things going.
for all who don’t know , the filioque is the Roman Catholic belief that The Holy Spirit proceeds from the father and the Son.
The concept is simply this :
[In some crazy world where water systems work like this] There are three components to this system namely The Sea, The Rivers and The Ponds. Now the Sea (Father) is the ultimate source of all water(Divinity). The water in the sea is not fixated in the sea but flows to the rivers and ponds. How this happens is that the water(Divinity) flows from the seas into the rivers (Son). The rivers then in turn allow for the water to flow to the ponds (Holy Spirit). Now it can be said that the source of the water in the pond is the sea. This is true as all water in this system finds its ultimate origin/source in the sea. However it can also be said that the water in the pond finds its source from the river because without the river, the water from the sea could not reach the pond. It is from the river that the pond receives its water. Thus it is true to say the water in the pond is from the sea and the river. The sea and the river are both components in the flow (Spiration) of water and thus they are one principal from which the pond received its water.
So the Filioque does not deny the Father’s singular role as the Cause (Aition) of the Spirit; but merely acknowledges the Son’s necessary Presence (i.e., participation) for the Spirit’s eternal procession. The Father and Son are thus collectively identified as accounting for the Spirit’s procession. This is all that the Filioque was ever intended to address; and it was included in the Creed by the Western fathers at Toledo in order to counter the claims of the 6th Century Spanish (Germanic) Arians. These Arians were of course denying this essential and orthodox truth, that is, the Son’s eternal participation in the Spirit’s procession and thus the Son being somewhat less divine than the Father
The filioque claims that the Holy Spirit also proceeds from the Son which if understood, is equivalent to the eastern formula " from the Father through the Son". The Catholic Church simply teaches that all 3 persons are eternal. They are equally God and only differs in rank according to relationships. The Father is the Father becasue he begets the son. The son is son because he is begotten of the father. The Holy Spirit does not beget nor is he begotten, but proceeds from the father and the son as from one principle. The main issue is the understanding of “as from one principle”. The Father is the ultimate origin of the Holy Ghost alone. However the procession of the the Holy Ghost involves the Son as the father gave everything to the Son except being the father. That is except the property to Beget. So the son inherits the Spirit of the Father as his own and the spirit is manifested through Son. As the Father is the origin of deity and in having the Holy Ghost proceeding, the son is a participant in transmission of being. Thus it is by way of the son that the spirit proceeds from the Father. He gets his being from the father and the Son as from one principle. That is what is meant to proceed from the son. The only reason the Holy Ghost proceeds from the son is because the Son is begotten of the Father. As such monarchy of the father is still maintained as everything is only becasue it has ultimate origin in the father.