score:34
I believe one reason for the order is because of the Great Commission in Matt. 28:19, in which it is written,
19 Therefore, go and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit.
ΙΘʹ πορευθέντες οὖν μαθητεύσατε πάντα τὰ ἔθνη βαπτίζοντες αὐτοὺς εἰς τὸ ὄνομα τοῦ πατρὸς καὶ τοῦ υἱοῦ καὶ τοῦ ἁγίου πνεύματος TR, 1550
Ontologically, the Son is begotten by the Father, and the Holy Spirit proceeds from the Father, but the Father is neither begotten nor proceeding.
In the creed established at the First Council of Constantinople in 381 A.D., the Lord Jesus Christ is described as “he who was begotten of the Father” (τὸν ἐκ τοῦ Πατρὸς γεννηθέντα), while the Holy Spirit is described as “the one who proceeds from the Father” (τὸ ἐκ τοῦ πατρὸς ἐκπορευόμενον).
Furthermore, the Holy Spirit proceeds from the Father through the Son (cp. John 15:26). Thus, the Father would be listed first, the Son would be listed second, followed by the Holy Spirit.