One thing that Trinitarians actually do have correct: The Father is not the Son. The Son is not the Father. They are different persons. Now if the Holy Spirit is a person, as they say, then the Holy Spirit is not the Father, and the Holy Spirit is not the Son.
Nevertheless, occasionally 2 Cor. 3:17 is used as evidence that the Holy Spirit is a person who is God: "The Lord is the Spirit."
Now it is provable that the Lord Jehovah is the Father, and it is provable that the Lord Jesus is the Son. Therefore, IF the HS is a person, "he" cannot be either Jehovah or Jesus! That is why the noted trinitarian scholar E. F. Scott (in his The Spirit in the N.T.) can understand
"Kurios ["Lord"] here [in 2 Cor. 3:17] to be Christ and interpret Paul as denying the personality of the Holy Spirit." - Word Pictures in the New Testament, A. T. Robertson, Vol. IV, p. 223.
Also the trinitarian The New International Dictionary of New Testament Theology, Zondervan Publishing, 1986, tells us:
"It is important to realize that for Paul too the Spirit is a divine power whose impact upon or entrance into a life is discernible by its effects." and, "It is important for Paul that the Spirit is a shared gift; it is a centripedal force [not a person!] drawing believers together into the one body of Christ. .... They are constituted the one body of Christ by their common participation in the one Spirit." - Vol. 3, pp. 701, 702. (Also see: Quotes: Holy Spirit is a Force from God, Trinitarians Admit; Search For Bible Truths)
Therefore to be 'one' with the Spirit results in being one with the Lord (whether it refers to Jehovah here, as I believe, or to Jesus as in most trinitarian interpretations. Having the active force of God, the Spirit, figuratively means having the Lord. Or as CBW, AT, and Moffatt translate 2 Cor. 3:17 "The Lord means the Spirit." Or, as the extremely trinitarian The New American Bible, St. Joseph ed. tells us in a footnote for 2 Cor. 3:13-18 -
"The apostle knows that his work is to result in the permanent presence of Christ among men through the power of the Holy Spirit."
And Thayer, also tells us:
"But in the truest and highest sense it is said ['the Lord is the spirit'], he in whom the entire fulness of the Spirit dwells, and from whom that fulness is diffused through the body of Christian believers, 2 Co. iii. 17.... to be filled with the same spirit as Christ and by the bond of that spirit to be intimately united to Christ, 1 Co. vi. 17...." - pp. 522, 523, Baker Book House, 1984 printing.
So we can see that even many trinitarians believe this particular scripture is saying that Jesus is figuratively the Spirit because union with that Spirit means union with Jesus.
Another possibility is shown by this trinitarian translation:
"the Lord [whether Jehovah or Jesus] no doubt is a spirit .... but we ... are changed unto the same similitude, from glory to glory, even of the spirit of the Lord [or 'just as the spirit comes from the Lord' - Lamsa]." - 2 Cor. 3:17, 18, Tyndale's New Testament, 1989, Yale University Press.
Not only do we never find anything approaching a clear statement of the trinity in the entire Bible, but in all the dreams, visions, etc. where we "see" God we never see a three-in-one God represented in any manner, nor do we ever see the "person" of the holy spirit (even though we often see the real spirit persons, the angels and Jesus, in association with that one true God). We nearly always "see" the heavenly spirit persons (God, Christ, angels) represented in human-like form. (E.g., Ezek. 1:5, 26; Acts 7:55.)
"The name ['angel'] does not denote their nature, but their office as messengers" - p. 38. "As to their nature, they are spirits.... whenever angels appeared to man it was always in a human form." - p. 39. And, "In...2 Cor. 3:17; 1 Tim. 3:16; 1 Pet. 3:18, it ['spirit'] designates the divine nature." - p. 593, Today's Dictionary of the Bible, 1982, Bethany House Publ., written by mainstream trinitarian scholars.
So we see God (who is a spirit person) always represented in human form and always as a single person, e.g., Ezek. 1:26 (Ezekiel could have easily represented him as three persons or even one person with three faces-compare Ezek. 1:10 -- but no Bible writer ever does such a thing! (Compare Dan. 7:9, 13) We nearly always see the spirit person of the resurrected Jesus in human form and always as a single person. We always see the individual spirit persons who are messengers (angels) of God as individual persons (and, incidentally, always with masculine, not neuter or feminine, personal names). But we never see the holy spirit as a person (and it is frequently represented as something that can be dealt out in multiple portions) - Acts 2:3, 4. (Also see: Is the Holy Spirit really a thing that can be poured out into portions?; Search For Bible Truths)
It is more than just odd that we "see" God (the Father only, Jehovah), we see Christ (the Son only, Jesus) with God, sent from God praying to God, etc., but we never see the neuter "person" of the nameless holy spirit in heaven with God or with the Son. (Also see: "Holy Spirit" in the Original Greek is Neuter - "It," "Itself" are Used in the Original New Testament Greek; Search For Bible Truths)
This could not be if the trinity doctrine were true. The inspired Bible writers simply could not so completely ignore as they have in the Holy Scriptures a person who is God.
There is no proper evidence (let alone proof) for the concept of the holy spirit being a person who is God.
This certainly should come as no surprise when we understand that the Bible writers all considered the Holy Spirit as an impersonal force sent by God. When a person rejects that force which God himself has produced and sent, then, of course, he is also rejecting the Most High God. This is why Jesus can equate the Holy Spirit with God and, at the same time (since Jesus is not God), show the superiority of God to himself:
"whoever says a word against the Son of man will be forgiven; but whoever speaks against the Holy Spirit will not be forgiven" - Matt. 12:32, RSV. (For more, see: Matthew 12:32 "whoever says something against the Holy Spirit will not be forgiven"; Examining the Trinity)
For much more, see:
Holy Spirit - Links To Information (Search For Bible Truths)
Exposing the False Reasoning Behind Holy Spirit 'Proof-Texts' (Search For Bible Truths)