The following is intended to correlate to classical scholastic terminology, to whit:
Nature = essence, as in "the Father, Son, and Holy Spirit all have the Trinitarian 'nature' of God."
Person = mode of particular operation, as in "the Son is the second "person" of the Trinity, light from light, true God from true God, begotten not made..."
The Father, Son, and Holy Spirit are all co-eternal and co-equal.
If the the persons of the Trinity - Father, Son, and Holy Spirit - are co-eternal and co-equal, and the Holy Spirit proceeds from both the Father and the Son...
Wouldn't the Father and the Son need to proceed from the Spirit as well in order to maintain the triad of equal procession from all three?
It seems as though, since the Holy Spirit doesn't have the faculty of bestowing procession upon the Father and the Son, then that gives the Holy Spirit one less faculty than the rest, which in turn subordinates the Holy Spirit to receive procession only.
Doesn't this infringe on the Spirit's co-equality?
This question derives from my study of the and drawn out debate concerning the validity of the filioque.