You are right, but the thing that is wrong is that the word "first" is associated with the number 1!

Think about it. Natural language could easily have associated the initial ordinal with 0. Let's call it the Nilth (zeroth is really hard to say).

The nilth element is element 0, the first element is element 1, etc.

The winner of a race is in nilth place. Silver goes to the person who came first. Bronze so second.

You walk in to a building on the nilth floor, climb the stairs to the first floor (that might sound weird to Americans but it's how it works in other parts of the world).

This is probably all sounding crazy to you but it's way more elegant and self-consistent.

Which century is the year 2023 in again?