#obviously there are other things influincing his decision (esp his tendency to still fall into that heaven/hell binary)

[ineffectualbookseller]

there is something to be said for how much the Metatrons' offer of restoring Crowley to an angel changed things for Aziraphale, even beyond the face value of the offer

Azirphale eventually (and reluctantly) accepts the promotion under the presumption that he will be able to change heaven - "if I'm in charge, I can make a difference."

and obviously, Muriel and Jim/Gabriel are two key narrative players to show us why Aziraphale would think heaven can still be reformed - Muriel who was unbelievably lonely in heaven and, despite all their ineptitude, is so excited to experience earth for the first time (the fondness in Aziraphale's face during their scene together in the bookshop is so touching) - and Jim/Gabriel who Aziraphle once knew to be cold, unsympathetic, and remorseless but after having the memories and influences of heaven stripped away turns out to be helpful, curious, and self-sacrificing (we see Aziraphale come to terms with this change over the season, telling Jim in e2 that he's really not sure if he's still terrible but when Crowley is questioning Jim in e5, Aziraphale's sure he's just being silly)

but even after witnessing this, Azirphale isn't jumping at the offer to run heaven. He says so point blank, "I don't want to go back to heaven," but everything changes when he gets the offer to restore Crowley as an angel

and clearly, Aziraphale is so excited by the face-value offer, he and Crowley would be safe and they'd be together, and Crowley would never be punished for doing good again. Just look at his happy little hands when he's asking Crowley to pause his confession so he can share his own great news. He's beyond thrilled to be able to offer this to Crowley, to live this life with Crowley (before he realizes it's not a life that Crowley wants - those happy hands are devastating in hindsight)

so if bringing Crowley to heaven with him was the selling point, why is he still going after Crowley says no? Because in Aziraphale's eyes, the power to restore Crowley is the power to correct heaven's mistakes. So heaven can make mistakes - Aziraphale thinks the Metatron just admitted that heaven is fallible

that is HUGE

(this is also not what the Metatron was saying - but in this context what Metatron said doesn't matter, only what Aziraphale heard)

and this isn't just coming from some angel - the Metatron is the voice of God. The closest thing to speaking to God we have witnessed since 2500 BCE in the Job minisode (the most recent evidence of God speaking directly to a character). Regardless of where God actually is during this story, Azirphale would be taking the Metatron's word as the word of God

Aziraphale has been acting against what heaven says God wants since the beginning: giving away his sword in Eden to protect Adam and Eve from their punishment (which he then lies to God about but is still allowed to stay on Earth), lying to save Job's children and openly question God's role in the plan ("I… I don’t think… that is what God wants"), and of course stopping Armageddon with his Great Plan vs Ineffible Plan pedantry (and before this, his plan for most of s1 is to get in contact with someone higher than Gabriel because of course, God wouldn't actually want this) - and when he is finally found out, Gabriel and Michael cut his ties with heaven

but now might-as-well-be-God is walking into his bookshop and scolding the middle managers and saying they've been fucking up. And he tells Aziraphale that they were wrong about him and they were wrong about Crowley and Aziraphale's the one that's been in the right

(keep in mind that Aziraphale does not know that the Metatron has been on the same subcommittees as the archangels - after Michael and Uriel don't recognize him, he's probably assuming they have very little contact)

if Corwley falling was a mistake maybe everything else Aziraphale has been internally questioning is too. If heaven can make mistakes than something has been going wrong in heaven - a fault in operations not in design - there must something to fix

Aziraphale is a being of faith and he carries such guilt for questioning that faith. The idea that the Metraton is acknowledging a mistake must be such a balm to him

It's really no wonder he thinks he can change heaven after that offer