I don't recall the Fathers using words like symmetrical, but if I am understanding you correctly, then you are on the right track to understanding what Orthodoxy teaches.
One father wrote (can't remember which) that each person has a characteristic unique to Him: The Father is the source, the Son is begotten, and the Spirit proceeds. Orthodox arguments regarding the filioque are ultimately patristic, scriptural, spiritual, and practical, and not based on theoretical or metaphysical arguments of symmetry or asymmetry, but the observation was made by a father, and I thought I'd pass it on.
I am glad that you have come to the realization that there are genuine substantive differences, and not just differences in terminology. Probably the most important thing that can come of these kinds of threads is an understanding of what the other believes.
Orthodox theology has been pretty highly developed by the Eastern Fathers, who were no slouches -- not in a systematic theology kind of way, but in terms of in-depth readings of the Scriptures and the earlier Fathers in order to understand the consensus teaching of the Church. Those of us on this thread who are Orthodox are steeped in that patristic mindset, and we already knew that the differences were substantive, and have tried to point this out.
Which is why these kinds of threads really don't go anywhere, which is OK, as long as we all raise a toast at the end and drink each other's health rather than get upset. If it hasn't been hammered out by now, I very much doubt that a bunch of armchair theologians in pajamas on FR are going to do so...
Thank you for your post. I will start a thread on the Filioque article and the Catachism in a minute.
A conversion, when happens, is never a result of some intellection. One who attempts to gain a convert with clever arguments is bound to fail. I remember my conversion. It happened through sheepish attendance at the Mass I did not understand. Questions came much later.
I am glad we are discussing this because it will give a better understanding of the Holy Trinity to both.