When you see these things in foreign languages, it may seem odd. However, if you look at the origins of words and phrases in English, it is also full of odd expressions. It is just that you are used to them.

Take "welcome."[1] Well come. You've arrived well. You make a good entrance? Not a ridiculous thing to say when someone arrives.

What about in response to "Thank you?" You are welcome.[2] Huh? What does that mean?

Or, "you are welcome to take a second cookie." How does that translate into "I do not mind if you take a second cookie?"

[1] Welcome translates quite literally in other European languages. For example, in French, it is bienvenue - bien: well - venu: came.

[2] On the other hand, it is much more common to say de rien (in French) or de nada (in Spanish): literally, "it's nothing."

The origin of "welcome" seems to be "will come", not "well come". This is clear from the German version "Willkommen", which is closer to the original proto-germanic "wiljakumo" and is directly related to the rather dated German expression "Will [er/sie] kommen!" ("Let him/her in, or "Will he/she come [in]!"), or even to English "will ya come!". The connection of "will" and "come" signals the desire to receive the guest.

The french "bienvenue" seems to be a too-literal translation from wiljakumo [0]. A similar construction is missing in Latin.

[0] https://en.wiktionary.org/wiki/bienvenue#Etymology

It is! I’ve been watching a bunch of Asian TV shows lately and I’ve seen that phrase crop up in both Thai and Taiwanese shows. I had the same question so I asked a friend who’s Thai about it. She said it’s equivalent to “I should get going”, “I’m going to head out”, or something of that nature.

Wait, so it's more "I go now" than "I go first"?

Well the other person hasn’t gone.

That underscores something about languages. They don't actually map 1:1 to each other. Whatever "I go first" means to speakers of Mandarin, we might only be able to approximate what that means in English.

An example that comes to mind is the oversimplification that happens when people say that the word "aloha" means "hello" and "goodbye". It only sort of does because that's how it is sometimes used. Really it's a whole concept that is unique to Hawaiian culture that would more accurately translate to "beloved" or "cherished".