I always wondered why Angel was saying all these bullshit lies about how he thinks humans should be in pain or whatever, but then I realized!!
It's a defense mechanism.
(analysis post / AKA me being lowkey delusional but whatevs)
So, like, this is when they first met. Think about it this way, you're Angel, and everyone avoids you because of your powers. You ask this guy for a napkin and he goes up to you, you're confused, question him, and he counters your statement by confirming that there is a way to be near you.
That obviously got to him, because, immediately after, the guy who never wants to do anything that bothers him, USES HIS WINGS TO DEFEND HIM FROM A GUN SHOT. A guy he just met by the way, and he verbally expresses that it hurts, but he did it anyway.
So then, they get teamed up together by Makima.
And here's the psychology of Angel. He hates death, hates seeing humans die, and he knows humans die if they get close to him, and he has this gut feeling about something he can't remember. So what's his best effort? Push people away.
Yes he's "lazy" (depression), but the way he was almost taunting Aki felt intentional.
Aki is the one human who wasn't scared to get close, so he wants Aki to dislike him so he'll have some other reason to stay back.
And it worked! Kind of.
---
And here's where it gets tricky. Angel has depression, for sure, and his powers are literally just for exploiting humans, so he just never wants to work, but he knows that if he gets attached to someone, he'll put in effort that he shouldn't. It's dangerous and bothersome.
He gets that point across in this scene, he's basically telling Aki that he wants nothing to do with him and anything he represents, and Aki is still hesitant.
So now, he has successfully created a distance between himself and Aki.
Or did he?
I really like this addition in the anime because it really gets across the point that I'm about to make.
Despite the walls they have created, they are curious about each other.
That's represented here well. Angel is literally creating a wall between them with his wing, but he's looking out at the city (that represents Aki) in wonder. Aki is almost analyzing him, despite the distance.
And that curiosity manifests into conversation, he wants to know more about him, and Aki listens closely to what Angel is telling him.
And then there's this scene.
Aki is holding onto him for dear life, and that puzzles Angel a bit. He keeps telling him it's fine to let him go, to the point where he even gets a bit frustrated as he explains how he doesn't care if he dies. But nonetheless he felt wanted, wanted alive, and that gave him a flashback of someone who wanted him dearly.
And then this happens!
He grabs his bare hand, and drags him to safety. And this is where Angel's true colors show because this shocks him but also angers him, he's angry, confused, and exasperated at the same time. he asks Aki is he wants to die, and Aki says that of course he doesn't, and asks him how much time he lost. Angel looks defeated as he tells him, and that's when Aki sorta gains an epiphany.
He doesn't want more death, he doesn't want to see people die in front of him, and that is something that Angel can relate to immensely. Suddenly, they had a lot more in common than they thought, and all of the barriers and walls Angel put up, Aki literally destroyed both socially and physically. In that last panel, Aki is holding onto him tightly, and Angel sorta looks defeated, he has gained an attachment.
---
After that, he once again, puts in effort in doing something for Aki's sake, and this time, it's disobeying Makima's order.
He fully accepts it, you know what, I am an angel, I do care. And he asks the mouse "is the city a good place", because he wants to know if caring is worth it, if putting this much effort into something reckless is worth it.
Then after that, he started to really put in effort into his job. Using his power despite his hatred towards it because people were in danger, collecting information and telling it to Aki.
Despite them growing closer, Angel is still a snarky little shit, but despite that, he cares. He acts like he doesn't, but he does and he knows it.
(I could also go on about how this parallels Reze and Denji's relationship but that's an analysis for another day)