It has long been established (by words of angels) that for every transgression and disobedience you commit you will have to receive the decreed (logical, natural, divine) consequence.
There is no way around that except through the power of salvation offered by God.
He then quotes Psalm 8:4-6 to point out that mankind, who is lower than the angels, may be crowned by God with glory and honor and set over the works of His hands. He sees this truth manifested in Jesus who, as a man, "lower than the angels"-mortal, was crowned with glory and honor so that he would be able to experience and overcome both physical death and the pain of spiritual death (the above named consequence) on behalf of each of us.
He says that the Father wishes to bring many of his children to a state of holiness (sanctification) and the way to do that was through making the captain of their salvation (Jesus) perfect through that suffering on their behalf, thus receiving, on their behalf, the decreed consequences, leaving us justified (all consequences received and experienced) in God's eyes, and open to holiness.
Both those who turn to Christ, seeking oneness of purpose with him and sanctification (holiness with no unpaid sins) made possible by Christ's gift to us and also Christ himself, who did make possible our sanctification, become one in this process. He is not ashamed to call us brothers and sisters. We become a package deal with him.
Paul quotes Psalm 18:2 and 22:22 to express what he envisions Jesus saying to us (a),
and what he says about the Father (b).
a. I will claim you as my family, and speak of that which is good about you, vouch for you, to the Father
b. I put my trust in God, trusting Him in His salvation for all who have come unto to me and who have changed, are living repentance, have been born again, into my (Christ's ) family
We are mortal. So was Jesus, who took on mortality that, through his death and the glory God gave him, he might destroy the post-death plans that the devil had for us. (The devil counts on our eternal spiritual death--separation from God because of our sins.) And so we do not have to fear death and the hellish bondage of separation from God, harrowed up by our sins.
Christ came to earth as a man so that he might be a merciful and faithful high priest (the high priests in the temple had the responsibility for offering sacrifices as payment for sins)-- offering a sacrifice for sin that reconciles us to God instead of being eternally separated (spiritual death) from him.
And, says Paul, Jesus fully understands what it is like to be tempted to sin, and so he is fully able to help us as we struggle with temptation. He understands.
And then chapter 3 is an exhortation to remain in that family of Christ, continuing in our repentance and in our confidence in him, and not hardening our hearts.