After discovering that there is no Biblical proof for this false doctrine, and after better understanding its pagan roots, the fastest, easiest way to DISPROVE the doctrine of the Trinity is by showing that the Son is subservient to (subordinate to or lower than) the Father, therefore they are NOT co-equal and that is the end of the Trinity doctrine. The Holy Spirit is ALSO subordinate to the Father which is further destruction of the false theory. However, we will later also show that there is no third God in One.

subservient:
1 : useful in an inferior capacity : subordinate
2 : serving to promote some end
3 : subordinate in capacity or function.

First, we must deal with this verse that seems to say that the Father and the Son are (or were) equal, but may instead be referring to Yahushua's former estate as Yahweh, the Son. Either way, it is no impediment to proving the subordination of the Son to the Father.

Who, being in the form of Elohim, thought it not robbery to be equal with יהוה [Yahweh, our god]: Philippians 2:6

If this verse is comparing Yahushua, the Son's current estate with his former glorified estate, they both could and would again be equal after glorification. Remember, it is the God Family and they share a family name (see here), so we don't know if this verse is referencing equality with the Father or with his former estate. If with his former estate, "isos" would mean equal to his (former) position without showing equality with the Father.

If, instead, it is referring to a comparison with Yahweh the Father, "isos" must mean something else. The Greek word translated as "equal" is "isos" ee'-sos probably from 1492 (through the idea of seeming); similar (in amount and kind):--+ agree, as much, equal, like. "Equal" was chosen by the translators to confirm the trinity doctrine (which was accepted doctrine at the time). But it could also (and better) be translated as "similar" or "like" or "agree". These words better fit what we discover below.

For as the Father hath life in himself; so hath he given to the Son to have life in himself; And hath given him authority to execute judgment also, because he is the Son of man. John 5:26-27

The previous verse clearly shows the similarity and difference between the Father and the Son. The Father has life in himself. The Son does not. But the Father has given this to the Son. THEN, the Son (still subordinate to the Father and possessing this gift) has a similar nature with life in Himself, but not of himself.

The Father loveth the Son, and hath given all things into his hand. John 3:35

This verse tells us that the Father is in charge of everything and owns everything. If the Son were equal, he wouldn't need to be given anything, he would already own it. The Father has the Son do His work. The Son (who was/is subordinate) didn't possess all until the Father gave it.

And he said unto them, When ye pray, say, Our Father which art in heaven, Hallowed be thy name. Thy kingdom come. Thy will be done, as in heaven, so in earth. Luke 11:2

Saying, Father, if thou be willing, remove this cup from me: nevertheless not my will, but thine, be done. Luke 22:42

I can of mine own self do nothing: as I hear, I judge: and my judgment is just; because I seek not mine own will, but the will of the Father which hath sent me. John 5:30

For I came down from heaven, not to do mine own will, but the will of him that sent me. John 6:38

It is the Father's will that controls, the Father is in charge, not the Son.

Some might argue that while Jesus was a man, of course he was subservient to his Father, the God. But before he became a man, he was SENT by the Father. The one who sends is boss over the one who is sent (the one sent is a servant). The ultimate (final) proof of the Son's subservience is after He has been restored to his heavenly position that he will still be subject under the Father:

For as in Adam all die, even so in the Messiah shall all be made alive. But every man in his own order: the Messiah the firstfruits; afterward they that are the Messiah's at his coming. Then cometh the end, when he shall have delivered up the kingdom to יהוה, even the Father; when he shall have put down all rule and all authority and power. For he must reign, till he hath put all enemies under his feet. The last enemy that shall be destroyed is death. For he hath put all things under his feet. But when he saith, all things are put under him, it is manifest that he is excepted, which did put all things under him. And when all things shall be subdued unto him [the Son], then shall the Son also himself be subject unto him [the Father] that put all things under him, that יהוה [the Father] may be all in all. 1 Corinthians 15:22-28

There is one body, and one Spirit [ed. the Spirit of God [Yahweh] that is possessed by Christ, meaning also the Spirit of Christ or the Comforter], even as ye are called in one hope of your calling; One Lord [ed. the Son], one faith, one baptism, One God and Father of all, who is above all [ed. including also, above the Son, even after being glorified and above the Spirit - "above all"], and through all, and in you all. Ephesians 4:4-6

But I would have you know, that the head of every man is the Messiah; and the head of the woman is the man; and the head of the Messiah is יהוה [Yahweh, the Father]. 1 Corinthians 11:3 (this is NOT equality)

Ye have heard how I said unto you, I go away, and come again unto you. If ye loved me, ye would rejoice, because I said, I go unto the Father: for my Father is greater than I. John 14:28

The Son is NOT equal but subservient to the Father and that ends the trinity doctrine, proving it false.

The next large (fatal) hole in the doctrine is to show that the Spirit is NOT a separate God.