He refers back to Hebrews 2:10, where it was said that the Father made the author of our salvation perfect through suffering. This has now been explained in the second half of chapter 2, in chapter 4:15, and again in this chapter in verses 6 and 7, and indeed it is an essential element of Christ being our high priest.
Christ is the author of our salvation, the source of it. No other Saviour but one who had perfect sympathy could undertake such a task. Our sins are so prolonged, so wilful, so unreasonable, that only perfect sympathy, perfect patience, and eternal commitment to his people could make Christ remain faithful to the end. We often see difficulty in the Lord forgiving a single sin, but we underestimate the Lord, for unless his love is truly vast, he could not pardon the mountain of sins that our lives present to him. We judge him by ourselves, but thanks be to God that he is so much greater than us.