Why is Jesus the right person to be God's rescuer? It might sound like a slightly strange question, but is the one that the writer of Hebrews wants to answer at the start of chapter 5. Why is he the fitting one, why is it appropriate to trust him, what made him suitable? He gives 6 main answers:
1. he was selected for the job of high priest by God v4
2. he was the son (ie the king) v5
2. unlike Aaron or any other high priest (or king) he was given the glory of an eternal high priesthood v6. The mediating work of every other one was compromised by the fact that they eventually died. Jesus Christ is alive for ever
3. he was subjected to weakness by becoming a man, allowing him to perfectly identify and deal gently with us in our weakness and ignorance v2
4. he offered acceptable and perfect sacrifice for sin v1
5. he submitted completely to God through the suffering this entailed v7
So he wholeheartedly identifies with us and is wholeheartedly identified with God, which makes him the perfect mediator. That is what qualifies him.
And therefore, as the writer says gloriously, he became the source of eternal salvation for those who obey him. Wow.