It's more about optimizing for curiosity [1]. Back-and-forths are fine when people are genuinely interested, but tit-for-tat spats are the worst. The former tend to continue while curiosity lasts, while the latter hopefully peter out after a while; in any case we should not be resuscitating them.

Push notifications are basically a stack-swap operation: they push down what you're spontaneously interested in right now, in favor of something you were interested in a while ago. This is good for engagement, but on HN we're in the sweet spot of not needing to juice engagement. HN is most valuable when it's as good as possible, not when traffic is highest [2], so we try for quality over quantity. (Not that the quality is particularly high, but that's a different story. [3])

I'm not sure that PG was particularly against notifications because he added this at one point:

Get notifoed when people reply to your comments on Hacker News - https://news.ycombinator.com/item?id=1203104 - March 2010 (55 comments)

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[1] https://hn.algolia.com/?dateRange=all&page=0&prefix=true&sor...

[2] https://hn.algolia.com/?dateRange=all&page=0&prefix=false&so...

[3] https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...

(p.s. Past posts by me about this - they just say the same thing but I'm listing them to save myself a search in the future:

https://news.ycombinator.com/item?id=27901918 (July 2021)

https://news.ycombinator.com/item?id=26597139 (March 2021)

https://news.ycombinator.com/item?id=22937472 (April 2020))