Trinitarianism asserts that the Son of God is coequal with His Father God and use these two statements as support: “making himself equal [isos 2470] with God” (Jhn 5:18); “thought it not robbery to be equal [isos 2470] with God” (Phl 2:6).
The Greek adjective isos is where our English isosceles—a triangle with two equal sides or legs—is derived along with skelos the Greek word for “leg.” It means “agreed,” “equal,” or “like” as it’s used in five other places in the New Testament: two groups of people being paid the same amount, “These last have wrought but one hour, and thou hast made them equal [isos 2470] unto us, which have borne the burden and heat of the day” (Mat 20:12); the agreement of eyewitness testimony, “For many bare false witness against him, but their witness agreed not [isos 2470] together … But neither so did their witness agree together [isos 2470]” (Mar 14:56,59); receiving a like favor in return, “And if ye lend to them of whom ye hope to receive, what thank have ye? for sinners also lend to sinners, to receive as much [isos 2470] again” (Luk 6:34); receiving a like gift from God, “Forasmuch then as God gave them the like [isos 2470] gift as he did unto us, who believed on the Lord Jesus Christ; what was I, that I could withstand God?” (Act 11:17); the heavenly city of Jerusalem having equal or like dimensions, “And the city lieth foursquare, and the length is as large as the breadth: and he measured the city with the reed, twelve thousand furlongs. The length and the breadth and the height of it are equal [isos 2470]” (Rev 21:16).
To understand in what way Jesus is “equal [isos 2470] with God” (Jhn 5:18; Phl 2:6), it must first be acknowledged that the Greek theos for “god” is simply a position of authority and not a kind of being. The Father is God because of His status as the highest ranking authority over all, including over His Son Jesus Christ. That theos isn’t a kind of being is evident by Jesus and Paul both using this word for different kinds of beings: “Is it not written in your law, I said, Ye are gods [theos 2316]? If he called them gods [theos 2316], unto whom the word of God [theos 2316] came” (Jhn 10:34-35); “For though there be that are called gods [theos 2316], whether in heaven or in earth, (as there be gods [theos 2316] many, and lords many,) But to us there is but one God [theos 2316], the Father” (1Co 8:5-6). Since a kind of being and a rank of authority are two different things, thus the Son can be “equal to” or exactly like His Father yet “not equal to” Him as God or rank of authority.
The Son was begotten in the exact likeness of His Father as the same kind of divine being, “For God so loved the world, that he gave his only begotten Son … the name of the only begotten Son of God” (Jhn 3:16,18). As the same kind of being, He had the power of God to create everything from nothing: “All things were made by him; and without him was not any thing made that was made” (Jhn 1:3); “God, who created all things by Jesus Christ” (Eph 3:9); “all things were created by him, and for him” (Col 1:16); “by whom also he made the worlds” (Heb 1:2).
As a human son is like his father in humankind but not equal in rank of authority, so it is with the Son of God and His Father. In the statement “but said also that God was his Father, making himself equal [isos 2470] with God” (Jhn 5:18), Jesus Christ’s claim of likeness with God was consistent with His earlier claim of having been begotten of God as His Son, “his only begotten Son … the only begotten Son of God” (Jhn 3:16,18). He was like God by virtue of having been fathered by God.
A little later Jesus stated “I and my Father are one” (Jhn 10:30), and was understood as claiming to be more than other men, “thou, being a man, makest thyself God” (Jhn 10:33). He claimed to be the Son of God sent into the world, “Say ye of him, whom the Father hath sanctified, and sent into the world, Thou blasphemest; because I said, I am the Son of God?” (Jhn 10:36). Like Adam, all men originate from this earth, but like God, the Son of God was sent to earth from heaven, “The first man is of the earth, earthy: the second man is the Lord from heaven” (1Co 15:47).
Dictionary.com defines the adjective like: “of the same form, appearance, kind, character, amount, etc.” This is how Paul used isos here: “Who, being in the form of God, thought it not robbery to be equal [isos 2470] with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men” (Phl 2:6-7). While in the form of God, He was like God. But having taken upon the form of a servant, He is now like men.
Trinitarianism, on the other hand, teaches “equal [isos 2470] with God” to mean coequal: “equal with another or each other in rank, ability, extent, etc.” as defined by Dictionary.com. It denies the way in which He is like God and confesses a way in which He is not. It denies His true likeness of having been begotten as the same kind of being and confesses a false coequality in rank of authority.