A Simple Refutation of the Filioque
The basic presupposition behind the Holy Spirit proceeding from the Son as well is the Biblical presupposition of "Everything the Father has belongs to the Son" (see John 16:15). Now aside from the fact that St. Gregory the Theologian clearly says that excludes causality1 which itself refutes the filioque, there's another issue at hand.
Florence is very clear when it dogmatically speaks that the Son is a cause of the Holy Spirit,2 this is undeniable. That being the case one question needs to be asked: Is the power of being cause a hypostatic property, or an essential property?
St. Gregory of Nyssa in his Ad Ablabium speaks of the mode in which something exists as a hypostatic property, since when we speak of for instance a tree, we are not asking how it was caused to exist but what its natural properties are which allows us to know it's a tree.3
Moreover, if causality was an essential attribute then that would just revive the Arian/Eunomian heresies since the basis of those heresies was the idea that being ingenerate was the essence.
In that case, being cause must be a hypostatic property, but this means only one hypostasis in the Trinity can be cause, which is the Father. If the Son gets the power of being cause from the Father (which Roman Catholic theology states that is the cause), and this power is a hypostatic property, that would mean that the Father is sharing a part of His hypostasis with the Son, which is why St. Photius refers to this as "Semi-Sabellianism".4
We have St. Gregory of Nyssa who will put the final nail on the coffin, because he explicitly talks about the non-transferability of hypostatic properties:
The characteristic of the Father’s Person cannot be transferred to the Son or to the Spirit, nor on the other hand, can that of the Son be accommodated to one of the others, or the property of the Spirit be attributed to the Father and the Son.5
This means that the Holy Spirit has His existence procession (that is, being caused in the manner of procession) from the Father ALONE even though in a temporal or eternal energetic sense we can speak of Him proceeding through the Son which shows such quote mines from the Bible and the Fathers about the Spirit proceeding through the Son actually proves the exact opposite of what it's intended to prove.
Recommended videos on this topic:
Filioque, and Why Orthodox Christianity Rejects It
8th Ecumenical Council, Filioque and Eternal Manifestation
Filioque: Its History and Refutation [The comprehensive one, also the longest video on this topic]
St Maximus the Confessor and the Filioque in Letter to Marinus
St. Mark of Ephesus Against the Filioque [Arguments St. Mark uses in Florence]
8th Ecumenical Council and its Rejection of the Filioque [Better version of the other 8th ecumenical council video]
Bad Filioque Arguments [Shortest video]
St. Gregory the Theologian, Oration 34 Everything the Father has belongs to the Son with the exception of causality.
Council of Florence, 6th Session: In the name of the holy Trinity, Father, Son and holy Spirit, we define, with the approval of this holy universal council of Florence, that the following truth of faith shall be believed and accepted by all Christians and thus shall all profess it: that the holy Spirit is eternally from the Father and the Son, and has his essence and his subsistent being from the Father together with the Son, and proceeds from both eternally as from one principle and a single spiration. We declare that when holy doctors and fathers say that the holy Spirit proceeds from the Father through the Son, this bears the sense that thereby also the Son should be signified, according to the Greeks indeed as cause, and according to the Latins as principle of the subsistence of the holy Spirit, just like the Father.
And since the Father gave to his only-begotten Son in begetting him everything the Father has, except to be the Father, so the Son has eternally from the Father, by whom he was eternally begotten, this also, namely that the holy Spirit proceeds from the Son.
St. Gregory of Nyssa, Ad Ablabium: But in speaking of cause, and of the cause, we do not by these words denote nature (for no one would give the same definition of cause and of nature), but we indicate the difference in manner of existence. For when we say that one is caused, and that the other is without cause, we do not divide the nature by the word cause, but only indicate the fact that the Son does not exist without generation, nor the Father by generation: but we must needs in the first place believe that something exists, and then scrutinize the manner of existence of the object of our belief: thus the question of existence is one, and that of the mode of existence is another. To say that anything exists without generation sets forth the mode of its existence, but what exists is not indicated by this phrase. If one were to ask a husbandman about a tree, whether it were planted or had grown of itself, and he were to answer either that the tree had not been planted or that it was the result of planting, would he by that answer declare the nature of the tree? Surely not; but while saying how it exists he would leave the question of its nature obscure and unexplained. So, in the other case, when we learn that He is unbegotten, we are taught in what mode He exists, and how it is fit that we should conceive Him as existing, but what He is we do not hear in that phrase. When, therefore, we acknowledge such a distinction in the case of the Holy Trinity, as to believe that one Person is the Cause, and another is of the Cause, we can no longer be accused of confounding the definition of the Persons by the community of nature.
Thus, since on the one hand the idea of cause differentiates the Persons of the Holy Trinity, declaring that one exists without a Cause, and another is of the Cause; and since on the one hand the Divine nature is apprehended by every conception as unchangeable and undivided, for these reasons we properly declare the Godhead to be one, and God to be one, and employ in the singular all other names which express Divine attributes.
St. Photius, Mystagogy, paragraph 9: And you should consider this: if the Spirit proceeds from the Father and proceeds also from the Son — O deceiving drunkenness of impiety! — why do not the Father and the Spirit beget the Son for the very same reasons — which will atone for this blasphemous chattering which turns the monarchy into many principles and causes! — and make common to all three hypostases what uniquely characterises the Son as well, combining the other two hypostases into one, in the same manner? And thus, Sabellius — or rather some other sort of monstrous semi-sabellianism would again sprout up among us.
Johannes Quasten's Patrology, Vol. 3, p. 267