I submitted the following to the "Orthodox-Catholic" Board, where it immediately got submerged by political commentary and facile attempts to defend the filioque by rejecting all application of reasoning to the Holy Trinity. I think the Eastern Fathers' reasoning on the question, as described by J. Pelikan, deserves a more thoughtful response than that. Anyone care to comment?
Jaroslav Pelikan, in his volume on the history of the Eastern Church, does a great job of explaining the reasoning behind the general consensus among the Eastern Fathers that the filioque should be repudiated.
To risk putting it in the form of a crude syllogism: The Holy Spirit must proceed either from the Essence (Ousia) of God, which is shared in by the three Persons (Hypostases) of the Godhead, or from one of the Persons of the Godhead.
That which is shared among the Persons is of the Essence, and must be shared in by all three Persons, not merely by two of the three. Therefore, if the Holy Spirit proceeds from both the Father and the Son, then He must proceed from the Divine Essence (from the Ousia of God). In that case, if one speaks of this in terms of the Persons of God, He must proceed from each of them equally, including from the Holy Spirit Himself. But, that is absurd; the Holy Spirit obviously cannot be said to proceed from Himself.
Therefore, the Divine cause of the Holy Spirit's procession is found, not in God's Essence, but is personal/hypostatic. In other words, the cause of the Holy Spirit's procession must be a Person of the Godhead, not God's interpersonal Essence. And the Scriptural witness and Tradition make it clear that, among the Persons, it is the Father from Whom the Holy Spirit most clearly proceeds. To suggest otherwise would be to attack the monarchy of the Father within the Holy Trinity.
The Eastern Fathers who wrote against the filioque argued that those scriptural passages such as that in which Jesus breathes on the apostles must be read as as symbolic references to Jesus' identity with the Father (not, of course, a literal, hypostatic identity, but an identity stemming from Jesus' absolute conformity to His Father's will), but not as "procession" in the same sense in which the Conciliar Fathers spoke in the Creed in affirming that the Holy Spirit "proceeds from the Father."
Succinctly put, the filioque is inconsistant with Trinitarian theology. According to Pelikan, the fine points of that theology were not fully grasped by Western theologians, who were less adept at, or familiar with, philosophical reasoning than were their Byzantine counterparts.