Biblical proof-texts for the Trinity are not proof-texts at all.

John 10:30 "I and my Father are one." This verse does not say that they are "same being." This text does not say how they are one at all. Fortunately for us, John later records Jesus' teaching on how He and his Father are one. "And now I am no more in the world, but these are in the world, and I come to thee. Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as (kathos) we are...Neither pray I for these alone, but for them also which shall believe on me through their word; That they all may be one; as (kathos) thou, Father, art in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me. And the glory which thou gavest me I have given them; that they may be one, even as (kathos) we are one: I in them, and thou in me, that they may be made perfect in one; and that the world may know that thou hast sent me, and hast loved them, as thou hast loved me" (John 17:11, 20-23). Jesus here makes clear that his disciples can be one even as (kathos) He and his Father are one. The Greek kathos means just as or how (See Strong's). In other words, Jesus prayed that they may be one just as He and his Father are one. If Jesus and his Father are one being manifest in two persons, for Jesus' prayer to be fulfilled his disciples must loose their identity and become absorbed into the Trinity! Assuming that a Billion or more will be saved (just for fun)--what will that make? A "Billinity"? So how are Jesus and his Father one, according to Jesus? The key is in verse 22: "And the glory which thou gavest me I have given them; that(hina) they may be one, even as we are one." The Greek word hina translated "that" literally means in order that (See Strong's). Jesus and his Father share the same glory and are thus one. Jesus prayed that his disciples may receive Their glory in order that they may be one with Them. There is no other passage of scripture in the Bible that defines how Jesus and his Father are one. The later post-Biblical doctrine that define the Trinity as one being in three persons is not derived from the Bible but is added to it. John 14:10-11 "Believest thou not that I am in the Father, and the Father in me? the words that I speak unto you I speak not of myself: but the Father that dwelleth in me, he doeth the works. Believe me that I am in the Father, and the Father in me: or else believe me for the very works' sake." As seen above, Jesus prayed that his disciples "all may be one; as thou, Father, art in me, and I in thee," but one need not go to a different sermon of Jesus to find this. He refers to this very concept in the same sermon. In verse 20 he said, "At that day ye shall know that I am in my Father, and ye in me, and I in you" (John 14:20). If Jesus meant for us to interpret "the Father [...] dwelleth in me" and "I am in the Father, and the Father in me" as "My Father and I are the same Being," did He also intend for us to interpret "I am in my Father, and ye in me, and I in you" that we, He, and His Father are all one ontological being? This, of course, is absurd. To complicate the issue further, Jesus concludes his sermon by saying "my Father is greater than I" (John 14:28). Such talk is nonsense if He and His Father are the same being. Colossians 2:9 "For in [Christ] dwelleth all the fullness of the Godhead bodily." Some have interpreted this scripture as meaning that all of the Trinity somehow dwelt in the person of Jesus in an ontological union of being as defined in the post-Biblical creeds. We'll now investigate that. First, one must understand that "Godhead" in 16th century English means "deity" or "godhood." The Greek word is theotes which means "divinity." This passage would better be rendered for our modern readers as "For in him the whole fullness of deity dwells bodily" (ESV). The scripture, therefore, is not stating that all of the members of the Trinity dwelt in Christ, but that Christ was fully and completely divine. Something else the critics overlook is the following verse. "And ye are complete in him, which is the head of all principality and power." The word translated as "complete" is the adjective form of the noun translated as "fullness" in the previous verse. For this reason, it is better translated "And you have a fullness in him..." This verse, understood this way, teaches that the fullness of divinity that was in Jesus can also be in us. This fullness was not reserved for Jesus only, but for all. Therefore, this scripture cannot be rightly interpreted to support the idea that God is three persons yet one being. The doctrine of the saints receiving a fullness of God is reflected in another scripture authored by Paul. "For this cause I bow my knees unto the Father of our Lord Jesus Christ, of whom the whole family in heaven and earth is named, that he would grant you, according to the riches of his glory, to be strengthened with might by his Spirit in the inner man; that Christ may dwell in your hearts by faith; that ye, being rooted and grounded in love, may be able to comprehend with all saints what is the breadth, and length, and depth, and height; and to know the love of Christ, which passeth knowledge, that ye might be filled with all the fulness of God." (Ephesians 3:14-19). 1 John 5:7 "For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one." This one is the most fascinating. Why? Because it is almost universally recognized as being an interpolation (addition) to scripture that wasn't actually written by the original author (See Metzger, Bruce. A Textual Commentary on the Greek New Testament, 647-649). Even if the text were authentic, which it probably is not, it does not define how the Father, Word, and Holy Ghost are one. For such a definition one must turn to John 17 which clearly shows they are not ontologically one being, but one in glory.