All of this. This is an excellent point, and I just want to add that this dynamic is so important to Lupin’s entire character arc in the series, and it pains me so much that people miss it so often.
Lupin is a very complicated character, but one of the core themes that surrounds him is the balance of personal responsibility and agency, and it’s a very strong theme because Lupin spends so much of his life denying his own personal responsibility. He’s in a position where he’s dangerous to those around him, and he was made that way by an assault against him when he was a child, which has left him with the perspective, rightly, that the fact that he’s dangerous isn’t his fault. He was assaulted and transformed by someone else, entirely stripped of his agency, and left to deal with the consequences.
Being faced by the prejudice of the wizarding world would only have reinforced that feeling. He ends up being shunned and punished for a state of being that he can’t help. It happens to him, and he can’t change that. And then Dumbledore turns up, a shining ray of hope that here’s someone who isn’t going to punish him for something he can’t change, who’s going out of his way to help him live a normal (ish) life (which explains why he is pathalogically incapable of admitting his own wrong-doing to Albus Dumbledore. Tell the first adult outside of his parents to believe him when he said he wasn’t a monster that he did something wrong? That’s like taking a saw to the branch you’re standing on when suspended over a bottomless pit. Counter-survival, every instinct ever says, DO NOT.). And then there’s James and Sirius, who are each very different versions of priviledged, wild and reckless with the invincibility of youth (James more than Sirius, I think), who take one look at his ‘monstrousness’ and are, basically, like ‘cool, that’s so badass’. They stick with him, they like him, enough to want to spend time with him, to teach themselves highly complex magic at an incredibly early age just to spend time with him when he’s at his most dangerous and monstrous.
I’m not surprised that Lupin let it go to his head. And it did, in a very specific way. Lupin ends up entirely conflating ‘it’s not my fault that I’m monster’ (which is true, not just because he didn’t choose to be assaulted, but also because, as a werewolf, he has no real agency) and ‘I am not responsible for the consequences of my monstrosity’ (which is false, because outside of full moons, Lupin is entirely responsible for how he handles his condition and the precautions he takes or doesn’t take).
He’s never, truly, been forced to face the consequences of what he’s capable of. Sirius (as is mentioned by OP) and James take the consequences for the flouting of the rules as teenagers. They would be the ones getting hurt by the wolf (in Lupin’s stead) to keep him corralled and to keep the consequences from reaching Lupin. The incident where Sirius nearly gets Snape killed via werewolf also doesn’t bring any consequences on Lupin. He had no agency there, either, no decisions he could have made that could have prevented anything, once again reinforcing the message that the danger he poses is not really his responsibility.
Now, I’m not saying that Lupin is aware of this, or delberately and callously being careless. He is, of course, highly and personally aware of the damage a werewolf can do to someone, to children, but there’s a subconscious separation going on where the werewolf is the aggressor, and Lupin is fully and entirely a victim in his own mind. Logically, he knows that he poses the same danger to others that he suffered, but it’s not real to him, not his responsibility, because he’s the victim. He’s been a victim not just of a werewolf, but also of society, and as much as he pays lipservice to acknowledging that people are right to be scared of him, I don’t think he really believes it, really feels it to be true, because he’s very very angry about the prejudice he’s suffered, and he’s not allowed to be angry because that would be just another sign of his monstrousness. And this sign is not one he could ‘other’ by separating himself from ‘the wolf’.
And Lupin has been stuck in this rut of conflated lack of agency with lack of personal responsibility for most of his adult life. What we see in the third book is, IMO, the painful but necessary beginning of the healing process. Lupin is forced to confront his own carelessness. He says as much when Harry confronts him about leaving, iirc (wish I had the patience to go looking for quotes like OP), he acknowledges the danger that he put Harry, Ron, and Hermione in. That he put every student in the castle in, if one of them happened to be in the wrong place at the wrong time. He acknowledges, at least to some degree, that he did have some agency in this situation. That he could have, and should have, done something to prevent the possibility of harm coming to those around him.
We don’t get to see what follows, not until much later, in book five (which I’ll admit I don’t remember as well as the rest), but it appears to me, in his behaviour with Tonks, that Lupin has, in his newfound revelation of personal responsibility, tipped too far the other way. He’s made another flawed conflation. He’s taken the reasons for his carelessness, the fact that he craved friendship, companionship, love, and marked them as just as bad as his carelessness. He’s gone from ignoring the problem because ‘It’s not my fault’ to ‘I cannot allow myself to have nice things in case I ruin them’.
And once again we see his avoidance tactics, although, again, it’s in the background of the background because Harry has bigger problems to worry about than Lupin’s love life. We see, in book six, that Tonks is grieving. Not Sirius, like Harry thinks, but Lupin, who isn’t dead, but is still, we can assume, lost to Tonks in some way. Because he’s rebuffed her, not because he doesn’t care, as we find out later, but because he’s taken on too much responsibility for his monstrousnes, and is, in effect, punishing himself.
And then, when confronted with Bill, who is a less severe version of Lupin’s own trauma played out right in front of him, except Bill gets to have what Lupin has spend his life alternately desperately grabbing for in neglect of those around him and denying in an attempt to overcompensate. Fleur stays. She tends Bill’s wounds and stands up Molly. It’s not the same, as Lupin himself says, but it’s enough, clearly, to break through some of his self-imposed isolation.
And then Teddy happens. And once again, Remus is confronted with the fact that his ‘carelessness’, the fact that he relaxed enough to let someone in, to let go of some of his guilt, has resulted in potential harm to someone (two someones) he loves. He’s once again making the mistake of conflating his responsibility with agency. There wasn’t anything he could have done to prevent this. Not with the knowledge he had in the situation he was in.
He runs away. He tries to cut himself off from soft, gentle things, tries to go back to being fifteen again. A monster, yes, wild and out of control and a danger to those around him, but safe because there’s someone else holding his leash. If someone else is responsible for pointing him in the right direction, he can’t be help accountable for his actions. (Sirius is not the only Marauder guilty of looking at Harry and seeing James)
But Harry is Harry, he is not James. And he tells Remus the one thing that he really needs to hear; ‘take responsibility’. And layered under that is ‘you deserve to be happy’, because what he’s telling him to do, what he’s telling him ‘taking responsibility’ is? Is going back to the people who make him happy, and just trying not to hurt them, doing his best not to hurt them. Accepting his lack of agency in his transformations, the lack of agency that made him into a monster in the first place, the fact that he is a victim, but also accepting his personal responsibility for what he does with that monster. He is the first person holding the leash of his own monster, and it’s up to him to keep it from hurting others without choking himself to death in the process.
TL;DR: I just really love Lupin’s character arc in the series and the way his journey was a messy and complex form of healing from his genuine trauma to his complete denial of responsibility to his unhealthy self-flagelation to an attempt at happiness that almos immediately backfired because of issues he’d only pushed aside rather than resolving to a revelation that he can be both a monster and happy, and that doesn’t make him a terrible person, as long as he takes responsibility for the monster his life made of him. (It’s a very, very good metaphor for the cycle of abuse, and I do love me a good magical metaphor.)
And it’s important to acknowledge that Remus absolutely did have a personal responsibility that he neglected in POA, that he had agency through the whole thing, and was wilfully careless with the safety of those around him because he couldn’t bring himself to fully face the danger he posed. It’s important, because without that, his entire character arc goes from an impressively realistic healing and redemption arc to something that just… falls flat.