I asked myself why the lectionary chose this particular passage for this particular Sunday. My supposition: the gospel lesson, John 12:20-33, is the main focus. So, I looked for connections and found several: glorify, high priest, Son, and death.
Glorify--the Greek word is doxazo, from which we got our word, doxology; also, means praise and honor. We can read the term in John's gospel to include crucifixion, death, and ascension, all of which would have been known to the hearers of this letter.
high priest--an intercessor, an intermediary between sinful humans and a forgiving God.
Son--Although Christians think of this term, of course, as denoting parentage, after all, we do say Father and Son, the psalm being quoted here, 2:7, refers to appointment. As Boring and Craddock put it in their NT Commentary, "Being 'God's Son' has roots in royal ideology....God grants to the king a place above all other monarchs and princes."
death--Jesus voluntarily submitted to the necessity for his death.
Being God's Son, in any way we consider this term, did not exempt him from suffering.
Having been made perfect [here, this term means "completed" rather than having achieved moral supremacy; see Hebrews 6:1; 7:11).
In stressing Christ's suffering, the writer of Hebrews may be trying to argue against the heresy that Christ was not fully human. He is not saying that followers of Christ should duplicate that suffering. Nor, should we ever cause suffering of our fellow human beings.