On understanding and other things
I think part of the reason why that final talk is so painful is because it shows that they don't know each other as well as they wanted to believe. Both of their ideas about who the other is and what they want are based mostly on what they want the other to be and not on who they really are.
They both want to be together, but in different ways. Aziraphale wants them to be on the same side, on the side of heaven. Crowley wants them to be on their own side, one apart from heaven and hell and everything they know, one where they can be themselves as Crowley and Aziraphale, not as angel and demon or even angel and angel.
And I think the reason they want such different things has to do with a number of things that could be summed up in their different life experiences and, consequently, their views on idealism and big changes.
Aziraphale never got over who they were in the beginning. I think for both of them that might have been one of the most beautiful moments of their lives, because they were still together, on the same side, simply in awe of the beauty of creation and unaware of the problems that would arise in the future. It is the only part of their history where they could be on the same side without breaking the rules, so it is only natural that Aziraphale remembers it as the best of times. But it ended with Crowley being unfairly cast out, so it's only sensible that he has a completely different perception.
And Aziraphale still believes Crowley to be an angel. He interprets his rejection of evil and his pursuit of goodness as a remnant of the angel he used to be and his desire to be one again. And actually, this interpretation makes sense, but it’s just not the correct one. Crowley has again and again denied his demon nature, doing everything in his power to do as little evil as possible without his head office noticing, yes, but not because he wants to be an angel.
Crowley has given up the idea of heaven as fundamentally good a long time ago, as it has proven, in more than one ocassion, to be capable of as much cruelty as hell itself in the name of an imagined greater good. Crowley's experience as an angel was good only at the very beginning. Once he learned that heaven was more about following rules than doing good, his idea of it was lost.
In short, Crowley doesn't want to be a demon any more than he wants to be an angel. It is not a matter of which side, but of the existence of sides per se. He does not like the system and does not want to be part of it from either side.
That is why he is hurt, because after so long, Aziraphale misunderstood his true nature. Crowley wants to be good, yes, but not in an angelic way. He doesn't want to go back to the place where rules and great plans matter more than real goodness. He just wants to be himself, outside of preconceived ideas of good and evil.
And so Aziraphale's offer to return to all that comes to Crowley as a disappointment. To realise that after all these years the one person you can consider a friend doesn't really understand you, the one person who has stood by you, listened to you, protected you, and done everything that no one else ever did. That even that person can't understand what you are, well, it must have felt like a stab in the chest.
And the same is true the other way around.
Crowley wanted to think that after the events of s1, Aziraphale had finally accepted who he was and what he (they) wanted. In the same way that Crowley hasn't been good at being a demon, Aziraphale hasn't been good at being an angel, and Crowley thinks that puts them in the same place. But it doesn't, because although Aziraphale is not just a clueless angel who silently follows the rules, neither has he been let down in the same way that Crowley has.
As I mentioned earlier, their difference of opinion is based (not entirely, but largely) on their different experiences of heaven. Aziraphale has been let down by heaven a couple of times throughout history, but none of them could match what Crowley had to go through when he was cast out. Aziraphale knows this, but he can never truly understand it.
So even when they both understand that heaven is not ideal, one of them approaches it with exasperating idealism, while the other doesn't even try anymore.
