Matthew 1:23 tells us that Jesus was to be called Emmanuel which means "God with us." How did the monotheistic Jews of the first century not compromise their belief that Yahweh God is the singular, eternal Creator by believing that the Father is God and Jesus is God? The New Testament reveals many obvious distinctions between Father and Son (ex: John 17; John 14:28). Jesus didn't pray to Himself. So if there is only one singular Person of God, then how could the Father and Son both be God if they are distinct from one another?
The doctrine of the Trinity was formulated in an attempt to reconcile the distinctions between Father and Son. The belief system known as Trinitarianism acknowledged that there is only one God and that Jesus is God but it redefined "one" to mean a unity of persons that are only one God in essence. It placed the distinctions as eternal and personal within God's essence instead of temporal and incarnational as the Word of God expresses. By temporal I mean that the Son didn't exist from eternity past but came to exist when God was manifest in the flesh. The singular Person of God is eternal as the invisible omnipresent Spirit, but as a man He had a beginning on a particular day when Jesus was born. We have learned in this video series that humanity is the distinction between Father and Son.
The doctrine known as Modalism teaches that there is only one God and that Jesus is God but does so in such a way as to deny or ignore the distinctions between Father and Son. Modalists don't believe the distinctions are genuine. Father and Son are looked at as just modes or manifestations that the singular divine Person of God switches between. He can manifest as Son one minute and then as Father the next. They make the mistake of saying that the Son is the Father and the Father is the Son. They deny that God is Father and Son at the same time.
But both of these views (Trinitarianism and Modalism) fail to maintain strict monotheism through a biblical understanding of the distinctions between Father, Son, and Holy Ghost. Just because there are distinctions does not mean there is not only one singular Person of God. While at the same time, just because there is only one singular Person of God does not mean there are no distinctions between Father and Son.
One other belief system is known as Nestorianism. Named after a man Nestorius of the fourth century who held this viewpoint. It teaches that the distinction between Father and Son is internal to Christ between His divine nature (the Father) and His human nature (the Son). The term Son is viewed to be only referring to the human nature of Jesus. This, however, ends up dismantling the unity of Jesus Christ's very Person (deity and humanity perfectly united in an authentic and genuine human existence).
The distinctions between Father and Son according to the Word of God are actually external to Christ. The term "Son" refers to Jesus' entire Person (the combined union of deity and humanity). God incarnate is the Son! If the Son didn't die as God incarnate, then how did God purchase the church with his own blood (Acts 20:28)? Sadly, many "oneness" believers are Modalist or Nestorian in how they communicate their belief.
Unitarianism teaches that there is only one single Person of God but they deny that Jesus Christ is God incarnate. They don't believe in the deity of Christ. They believe that Jesus is the Son of God, but fail to understand that this means He is God incarnate. They argue that because Jesus had a God that He can't be God according to John 20:17. This is the most extreme in its error because it denies that Jesus Christ is the great I Am (Yahweh incarnate). Having someone indwell you and being that very someone are two entirely different views of Jesus' identity.
But we can believe in strict monotheism while avoiding these different belief systems by acknowledging the distinctions between Father and Son and placing them in their proper place. Since the incarnation the singular God now exists in two ways at the same time: as God and as man. The subject of Christ is the singular God. Everything Jesus did was "God incarnate" doing those things. Not just human nature alone or deity alone doing those things. Jesus is God Himself existing as a genuine man. The personal subject of all of Jesus' actions is God. Jesus is God existing as man while we are man existing as man. God literally joined human nature to his divine nature in order for His very Person to genuinely become man. He still exists as the eternal invisible God outside of the incarnation, but also came to exist and experience life as a man with a genuine human mind/consciousness through the incarnation. The deity of the Son and the deity of the Father is the same singular Person. But they are distinct in their type of existence. Father refers to God's divine manner of existence while Son refers to God's human manner of existence.