Shared ground
Hebrews 7:20–22 adds a new support to the claim that Jesus’ priesthood is stronger than the earlier priesthood: it rests on God’s sworn oath. The text contrasts priests who became priests “without an oath” with the one whom God addresses with a public promise: “The Lord swore and will not change his mind.”
The passage then draws a conclusion: because Jesus’ priesthood is oath-backed, he has “become the guarantee” of a “better covenant.” The argument assumes that an oath, especially one God will not revoke, makes a commitment firm and dependable.
Where interpretation differs (only where needed)
What “better covenant” mainly means. Some take “better” to emphasize improved effectiveness: the new covenant actually accomplishes what God intends (especially secure access to God and lasting reconciliation). Others take “better” to emphasize permanence: it is better because it cannot be replaced, since it is anchored in God’s unchangeable oath and an eternal priest.
What “guarantee” means in practice. Some read “guarantee” as Jesus personally securing God’s promise for his people—his role and status make the covenant reliable. Others read it more as Jesus being the pledged basis or “security” of the covenant itself—his priesthood is the concrete assurance that the covenant will stand.
Why the disagreement exists
The text gives a clear logic (oath → permanence/reliability → “better covenant”) but uses compact terms: “better” is comparative without spelling out every dimension, and “guarantee/collateral” can be understood either as a person who guarantees or as the pledged security. Also, “they” (priests without an oath) could be read broadly (the Levitical priesthood as a whole) or more narrowly (the normal way priests were installed), which can affect how strongly the contrast is pressed.
What this passage clearly contributes
This passage explicitly ties the superiority of the covenant to God’s oath establishing Jesus’ priesthood: God swore, will not change his mind, and therefore Jesus’ priesthood is lasting (“forever”) and dependable. On that basis the writer makes an explicit conclusion: Jesus is the guarantee of a better covenant. The theological inference the author invites is that the covenant’s stability does not rest on changing human office-holders, but on God’s unrevoked promise regarding this priest.