Being co-equal is not intended as a mathematical equality and does not necessitate that none is in charge of another.
The scriptures talk about the equality of the Father and Son in John 5:18, where John states "For this reason therefore the Jews were seeking all the more to kill Him, because He not only was breaking the Sabbath, but also was calling God His own Father, making Himself equal with God."
The equality mentioned here obviously has nothing whatsoever to do with authority, since the equality is the equality of a father and son, and it is understood throughout the scriptures that fathers have authority over their sons. I believe here John is referring to equality of essence: they are equally God.
The Athanasian creed talks about the co-equality of the three members of the Godhead in terms of their glory -- they are equally glorious and equally deserving of glory.
There is no suggestion in the scriptures or in any orthodox Christian theology of the Son being just as in-charge of the Father as the Father is in-charge of the Son. The three persons of the trinity have three distinct roles, just as a human father has a different role than his human son does.
The trinity, in brief, can be summarized by the following three points:
1. There is only one God.
2. He is co-existent in three persons.
3. Each of these three persons is eternally distinct.
We believe this because the Bible teaches that there is only one God, that the Father is God, the Son is God, and the Holy Spirit is God, and we see from scripture that they each have different roles within the Godhead.
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