The Spanish words are very similar to the English ones:

- Autorización : Authorization

- Autenticación : Authentication

- Autoridad : Authority

- Auténtico : Authentic

I would guess that in other romance languages, they are also similar to the English version.

"Log In", on the other hand, only makes sense in English. If you tell someone "Estoy registrando adentro" they will be dumbfounded.

Language families other than romance and germanic exist.

And programmers who work in those languages are more than welcome to use terms that make sense to them! There is zero reason to change terms that are perfectly clear to English speaking programmers simply because not everyone speaks English (or languages where English got its words from).

"Estoy registrándome dentro" (I'm signing myself up) it's totally fine. The problem lies on that the phrase looks like you are signing up first, and not logging in to a previous account. In Spanish you would just say 'enter in your account'.

I can't imagine learning German or some similar language and complaining that their words aren't clear just because I don't speak German fluently enough.

The point OP is making that those words are intuitive for readers (everyone). Knowing language is one thing, but intuitively making sense of similar words in a new context is another. Most non native English speakers think in their own language. Seeing word “authorization” simply doesn’t evoke the link with “authority” in their own language.