Yeah, I mean if I were Sam, I'd honestly feel more comfortable bringing up something symbolic like this because it allows it to live in this strange world of safer(?) abstractions.
I mean, there he is, pointing out something he passively "did" as a mere infant (being born, being targeted by Azazel) as a way to bizarrely equalize himself and Jack. It feels like a very forced way to parallel them.
A closer parallel could've been when soulless Sam almost sacrificed Bobby, or when Godstiel called them nostalgia and almost moved to kill them, or when Demon Dean was seconds from bashing Sam's head in with a hammer, or when Mary almost blew Sam and Dean's brains out while under the MoL influence, etc etc.
These "almosts" are soooo much closer in nature to what actually happened than Sam pivoting to the circumstances of his birth! "I killed mom" has the same abstract feeling of self-worthlessness that "not being pure" does. It's inherent. Inevitable. Uncontrollable. Just a fact of life. Passive.
Aside/// Sam's internalized hatred of "ever being born" doesn't happen in a vacuum, for sure. This is something that numerous characters also blamed Sam for, like the clever "aside" to the audience in the "Nutcracker" game during Changing Channels:
GAMESHOW ANNOUNCER: Would your Mother and Father
still be alive... if your brother was never born?
(The answer is, of course, at least in Gabe's world: yes.)
But it's still interesting to me how it unintentionally allows Sam to sidestep... a lot of real decisions, like what you mentioned, the Emma thing.
It also allows him to sidestep his not-decisions, like doing nothing after Kevin got kidnapped. Even later, when Sam focused on "letting Dean down so hard he had to turn to other brothers," he doesn't explicitly mention his abandonment OF other people, like for example Kevin.
Crowley does this exact same thing imho when he rants about Kevin's (lack of) safety being mostly attributable to The Winchesters (TM) positioning himself as the wise, savvy one who "warned Kevin" of the danger (no matter that Crowley tortured Kev and killed Kev's relatively harmless fellow students. Not to mention tortured his friggin' mom). If memory serves, Cas calls Crowley out on this, lol.
Anyway, later when Lucifer mentions "the Amelia and the dog thing," Kevin does not feature there either, at least not obviously? By contrast, with respect to Dean's feeling of guilt and also the later assignment of blame for Kevin's death by Sam, Crowley and Metatron: Kevin gets mentioned a good bit! Usually directly TO Dean. Surprise, surprise.)
I personally think it'd be much more emotionally trying for Sam to bring up actual things he's done over the years (something-something human sacrifice, almost killing Bobby, Emma, that one Lester dude he preyed on, Oskar, etc.)
It reminds me a bit of his words in Tombstone to Jack:
Sam takes a deep breath, trying to follow up all that heavy honesty with his own wisdom. This time, he tries mimicking Cas’s earlier words, which seemed to work in the car. (Notably, he misses them mark because he’s not specific like Cas was. Cas underlines that he’s killed people he loves, but Sam keeps it vaguer: “Things we regret.”)
And with Sam, Jack shuts down again. He’s sharp about it this time. Jack’s body language has Sam reeling back, hands up.
transcript:
SAM: Jack, look, this life, what we do, it's… it’s not easy. And we’ve all done things we regret.
JACK (very sharp): Just don’t.
So yeah, while a feeling of inherent self-worthlessness is absolutely crushing in its own right, I think it's fascinating to consider that in some ways, it allows for an abstract "original sin," that allows Sam to look away from his actual mistakes.
(And again, I suppose we're all a little bit like this as humans. It's hard to admit when we fail, so I have sympathy!)