Commenting on Heb 2:10, Catholic scholar Mary Healy offered the following comments on Jesus and His becoming "perfect":
What does Hebrews mean by saying that Jesus had to be made perfect? The author seems to be using this verb in three senses. First, “make perfect” (teleioō) is related to the adjective “perfect” (teleios), used in the Septuagint for human beings who are morally blameless and upright (Gen 6:9; 1 Kings 15:3) and for animals that are whole and unblemished, worthy to be offered in sacrifice to God. That Jesus had to be “made perfect” does not mean that he was ever morally flawed; rather he freely chose to take on human nature in its fallen state, with the weakness, pain, and death that are intrinsic to it, and through suffering to perfect it in holiness. It is easy to be virtuous when all goes well and people treat you kindly, as Jesus himself noted (Luke 6:32-34). But human virtue comes to perfection only when it is tried and tested by suffering. In enduring his passion, Jesus allowed all the evil unleashed upon him to bring forth the most perfect act of love, trust, and obedience to God that could never come from a human heart. In the furnace of suffering his human nature was refined to limitless perfection. He was thus qualified to be offered in sacrifice as the perfect, unblemished Lamb (1 Pet 1:19).
Second, Christ was “made perfect” in that his human nature was transformed by his entrance into divine glory (v. 9); or to use a patristic term, he was “divinized.” By becoming man he assumed our nature, which was subject to weakness and deprived of the heavenly glory for which it was made (see Rom 3:23). As Jesus affirmed in the Gospels, his passion was therefore necessary as the God-appointed means for him to ascend to divine glory (Mark 8:31; Luke 24:26). So too for his followers, the path to glory is usually through suffering (2 Cor 4:17; Phil 3:10-11; Heb 12:10-11).
Finally, there is a further significance to teleioō. In the Septuagint, this verb is used to translate the Hebrew expression meaning to “ordain” a priest (Exod 29:9; Lev 8:33; Num 3:3). As Hebrews will proceed to show, Jesus is the great high priest (4:14), and his rite of ordination is the cross. (Mary Healy, Hebrew [Catholic Commentary on Sacred Scripture; Grand Rapids, Mich.: Baker Academic, 2016], 62-63, emphasis in original)
Tying Jesus’ “becoming perfect” with our becoming perfect in Heb 10:11-13, Healy offers the following insightful commentary:
Several times Hebrews has used the term “make perfect” (teleioō) to express how Jesus was transformed by his passion (2:10; 5:9; 7:28). Here the author reiterates what Christ’s sacrifice has accomplished by sing this term in a new way, now applied to his people! For by one offering he has made perfect forever those who are being consecrated. This suggests that the same three senses of teleioō that applied to Jesus (see comments on 2:10) also apply to those “many children” he is bringing to glory; they are made holy and pleasing to God, they are made shares in divine life, and they are ordained priests of the new covenant. This is confirmed in verse 19 below, where Hebrews declares that believers have a privilege surpassing that of the high priest of Israel: we can freely enter the sanctuary, the presence of the living God—and not only one day a year but always. The whole life of Christians is now qualified to be a priestly life, in which all our actions and sufferings can be offered as “a sacrifice of praise,” that is pleasing to God (13:15-16; see 12:28-29).
Hebrews refers to believers with the same term “consecrated” (or better, “made holy”) as in verse 10, but now with a different verb tense. Whereas verse 10 said we have been made holy (an already existing state), verse 14 says we are being made holy (an ongoing action). Again there is the paradox of the “already” and the “not yet.” The sacrifice of Christ truly has uprooted sin from the human heart and cleansed the conscience of all who believe in him. But believers must appropriate and live this new freedom. We are like a paralyzed person whose nervous system has been restored through surgery: the disability has been removed, but now the person must learn to use muscles unaccustomed to walking. In Christ, believers have a new ability to resist sin and obey God from the heart, which now has to be exercised. As Paul says, “You also must consider yourselves dead to sin and alive to God in Christ Jesus. Let not sin therefore reign in your mortal bodies” (Rom 6:11-12 RSV). (Ibid., 205-6, emphasis in original)
Heb 10:10-14 is often abused by Reformed apologists to support their view of the atonement (definite atonement) and perseverance of the saints. For a refutation, see the exegesis of the pericope at: