Why must the redeemer be truly human?
That in human nature he might on our behalf perfectly obey the whole law and suffer the punishment for human sin; and also that he might sympathize with our weaknesses.
Therefore he had to be made like his brothers in every respect, so that he might become a merciful and faithful high priest in the service of God, to make propitiation for the sins of the people.
Hebrews 2:17
The trouble we may have with reconciling the paradox that is seemingly present in the hypostatic union of Christ is not a new thing. Some of the earliest heresies taught that Jesus was not God at all - not Creator, rather a creature (see Arianism and Ebionitism). Others taught that he was part man and part God - a demigod akin to Hercules (Apollinarianism, Nestorianism, and Monothelitism). And still others taught that Jesus was actually God, but that he wasn’t actually man - he just appeared to be a man (Docetism and Monophysitism). But Scripture teaches us, and the early ecumenical councils affirmed, that Christ is fully man.
The author of Hebrews doesn’t just state this as-a-matter-of-fact, but as a matter-of-necessity. The author states that Christ had to be made like us in order to make proper-propitiation (say that 10 times fast!!) for our sins. The implication is clear: if Christ was not made truly man in the incarnation then we are still in our sins (not unlike Paul’s claim that if Christ has not been raised from the dead, then we are still in our sins (1 Cor 15:17)). He did not simply appear like a man, or put on a temporary cloak of flesh - he took on flesh permanently.
This should strike us as profound. The fact that there is no inherent obstacle to God becoming man in the incarnation, to the Creator becoming a part of His creation - this should elevate our understanding of what it means to be human. Mankind is created IN the image of God (Gen. 1:27), and Christ IS the epitome of that image (Col. 1:15).