How do we show terms like “Father” and “son of man” cannot be used as “proofs” of a plurality of persons in the godhead?
The biggest problem is seeing how these terms are used everywhere else in the OT. Making sure we correlate or let Scripture interpret Scripture is necessary. We believe in a single divine Author. We really believe all Scripture is inspired, that holy men of old wrote and they were moved by the Holy Ghost. If that is the same belief of the seeker you’re dealing with, start with showing how these terms were used in the entire OT.
For instance, how is Father used in the OT? God is seen as Father by virtue of creation (Deut. 32:6). He is the Father of Israel (Jer. 31:9; Ex. 4:22; Hos. 11:1-4); Father of the King (2 Sam. 7:14); Father of each individual Israelite (Mal. 2:10). So all of these passages show that Father is “Creator—creation” language, not divine persons.
The term “son of man” is used 70xs by Jesus Himself. Rushing to Dan. 7 as a proof of a cosmic trinity is problematic, again because that’s not the only use of the term in the rest of the OT. Multiple passages show that the term “son of man” applies to human beings (Num. 23:19; Job. 25:6; 35:8; Ps. 8:4; 80:17; 144:3; 146:3; Is. 51:12; 56:2; Jer. 49:18, 33; 50:40; 51:43; Ezek. 2:1, 3, 6, 8; 3:1, 3, 4, 10, 17, 25; 4:1, 16; 5:1… and the list could go on and on.) The overwhelming biblical evidence is “son of man” refers to human beings. Specifically in Dan. 7 the son of man is “given dominion, given glory, given a kingdom” which means the son of man cannot be about a co-equal person. One person of the trinity cannot empower, give, establish, or impart anything to another. But, the man that God became can be given granted dominion through HIs obedience.
These OT and NT terms must be interpreted from God’s Self-revelation. The Bible shows how these terms must be understood and used. This has led Catholic scholar Edmund Fortman to admit, “Jesus did not invent the term ‘Son of Man’… Does the title affirm Jesus’ divinity? No…” In Gal. 3:24 Paul writes by the Spirit of God, “Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.” We cannot be led to the man that God became, Who is the only saving sacrifice, the only High Priest, with the One saving name of Jesus… if we don’t let the OT show us how to be led to Christ.