On the topic of the Filioque: I haven't seen the Catholic point-of-view put forward inasmuch as procession is concerned, so I'll have a go. Generally speaking, outside of the Fathers, one of the best sources of understanding the whys of the Catholic faith is the Angelic Doctor, St Thomas Aquinas. In his Summa Theologica, Part 1 Question 36 deals with the Holy Spirit. He asks and answers the following questions:
1. Is the Holy Spirit the proper name of a Divine Person?
2. Does the Holy Spirit proceed from the Father and the Son? (more specifically, does the Holy Spirit proceed from the Son?)
3. Does the Holy Spirit proceed from the Father through the Son?
4. Are the Father and the Son one principle of the Holy Spirit?
The answer to all of these, according to Aquinas, is yes. The first topic isn't something anyone disagrees on (in this thread, anyway), so we'll leave it be, and I'll attempt to explain Aquinas's arguments for 2, 3, and 4.
Earlier, Aquinas establishes that the persons of God, because they are one in essence, can only be distinguished from each other by their relations to each other; that is, the Son is distinguished from the Father because the Former is begotten eternally of the Latter. By this logic, if the Holy Sprit proceeds from the Father alone, then nothing distinguishes Him from the Son, since they are one in essence, as the Father and the Son are one in essence.
Therefore, Aquinas argues, the Holy Spirit and the Son must have opposite relations to each other, which must be relations of origin (established in Question 28), that is, one must proceed from the other. Nobody (that Aquinas knew of, or that I know of) confesses that the Son processes from the Holy Spirit, so the Holy Spirit must proceed from the Son.
Now, 3 and 4 address the question of the phrasing through the Son, which you have noted, Anastasia, would be acceptable to some Eastern Orthodox. As noted above, Aquinas also argues for this phrasing, what might be called "ex filio" as compared to "filioque" in the same part of the Creed.
To grossly simplify Aquinas's argument for ex filio, he points out that the preposition "through" can refer to many different relations of things to an action. For example, we can say that an artisan works through love of gain (a final cause), or through love of art (a formal cause), or even through the command of another (a motive cause). All of these refer to why an artisan works. But we can also say the artisan works through his tools, which does not refer to why he works, but how he works. And it is in this sense that we say the Holy Spirit proceeds from the Father through the Son.
Finally, on the topic of one principle: Aquinas argues that the Father and Son are one principle of the Holy Spirit because they are one in all things except their relations to each other; that is that one is Begetter and one is Begotten.
On a side note: Aquinas also asserts that the term "proceed" can refer to taking origin in any way, thus why he does not appear to have argued for "ex filio" to replace "filioque" in the Latin translation of the Creed. To draw on the artisan metaphor again, one can rightly say that a sculpture comes from the artisan and his tools, while understanding that really, the sculpture comes from the artisan's mind, through his tools.
I hope all of this makes sense, but in short, I think there needs to be frank and open dialogue about what the Churches teach and do not teach. For example, some Catholics would argue that the Holy Spirit proceeds from the love between the Father and the Son, which is completely at odds with any patristic or Thomistic understanding of the Trinity, and not actually taught by the Church. But an Eastern Orthodox may hear this, and be hardened in heart because, well, what need do you have of other witnesses when you hear the error from their own mouths? So without realizing it, both of them have hindered hopes of reconciliation.
All of this aside, whether the Roman Bishop had the authority to insert this into the Creed is another debate entirely.
