My best guess would be familiarity, a connection to the real world.

When you go into a physical location, say visiting a hospital or business, you "sign in" and "sign out" of that place.

When you participate in an activity, for example a class or sports club, you "sign up" to join.

Probably because the term SSO (Single Sign On) was coined and used "sign", and the various "Sign in with $BigTechCompany" buttons are everywhere, so "logout" started conspicuously not matching.

I've had some users confuse the terms. We use register, log in, logout now.

Sign up and sign in confused some people because of how it mentally translated to some people's native language. We targeted more elderly people too, who didn't know the difference.

I assume that log in and log out might translate poorly to some other languages. Lots of people optimize heavily on registration, like even a 1% difference can be significant. And copy is low effort, so I assume there's a reason it evolved this way. Maybe it's a hint on which market the website targets.

log in is too technical. over two decades everything has been marketed to as many dumb dumbs as possible.

That's an interesting question. Especially, I would associate "signing up" more with a paying subscription then I would a registration or an account creation

And who knows why I always have to search for the login link? Sure, new accounts are cool, but existing members should be treated better

to me its because there is sign up in and out. but there is no log up. for me it brings consistency.

Concerns over deforestation has made logging less socially acceptable?

Because it’s more colloquial. Login sounds more technical. It doesn’t pass the Chinese immigrant mom test. If I tell her to login, she will be confused. If I tell her to sign in, there’s a better chance she’ll understand

Because it's hard to pronounce the "L".

I always though it was because it was easy to confuse with logging.