If Jesus and the Father are not distinct Persons, why are there clear passages showing a subject-object relationship between them?
This argument is based on any distinction made between Father and Son whether of messianic prophesies in the OT or Father/Son statements in the NT such as, “I (subject) have glorified thee (object) on the earth: I (subject) have finished the work which thou (object) gavest me to do” (John 17:4). The point made in this argument for the trinity is as follows: Father and the Son stand in an “I”–“You” relationship of each other. The Son personally relates to the Father, so there must be two persons here.
The “subject/object distinction” argument is being dropped by more and more scholars as regard to speaking of “persons” in a trinity. As a matter of fact, one example of this is well-respected Southern Baptist theologian Frank Stagg who says the NT doesn’t make room for the concept or even the term “persons.” He goes further, saying this led to worship of three distinct gods.” To the term trinity were soon added the terms persons, three persons, three persons of the Godhead, and even the ranking of the persons as first, second and third. Thus, trinitarianism was fast on the way to tritheism, a de facto belief in three distinct gods. This is something the New Testament never anticipated and does not support. (pg. 8, Baptism of the Holy Spirit).
This distinction cannot be about separate persons. First, in the OT the clear “prophetic nature” of the Psalms and other OT passages is readily admitted by scholarship of every denominal and theological stripe. This acknowledgement proves these messianic Psalms are speaking prophetically or futuristically of the incarnation, not an “eternal son.” This is proven by the content of the prophesies themselves. Both these passages as well as the NT repetitions show the Son would: be begotten, love righteousness, hate iniquity, be a High Priest (only men could be Heb. 5:1), is exalted (a co-equal god could not be), etc.
So, the context of these passages are references to Christ speaking of His existence and work in a future time. He could not be begotten, prove He loved righteousness (this is action played out on Earth as a man), hated iniquity (again as shown on Earth), is a priest forever, or be exalted, from eternity past. So, the subject/object distinction is about the incarnation and what His work was as man.
John 17:4 in particular speaks of “glory” the man Jesus accomplished. Remember, this passage is in the context of prayer and so cannot be about one god praying to another god. That cannot fit a co-equal trinity. Heb. 5:7 shows clearly it’s about the man Jesus praying. All of the messianic psalms and OT verses speak of a future time when God would be truly a man. All the NT texts dealing with Father/Son language do not speak of a so called “eternal son” but the man who would accomplish His work as the final Adam!