when and how did the word “retirement” become what it is today? Wouldn’ retire mean to get tired again like rehire means to hire again.

withdraw, retreat
Middle French retirer, from re- + tirer to draw
Date: 1533

It comes from the French word for “withdraw.” Its first cited usage, in the sense of “to withdraw from office or an official position; to give up one’s business or occupation in order to enjoy more leisure or freedom (esp. after having made a competence or earned a pension),” dates from Pepys’ diary (1667).

Earlier uses meaning “to withdraw to or into a place (or way of life) for the sake of seclusion, shelter, or security” date from about a century prior to that.

The verb tire, meaning to become exhausted, comes instead from Old or Middle English (it’s unclear).

If some one tires me more than once I can say “You are re-tiring”
If some one treats me to ice cream I can say “will you re-treat me?”

In Spanish “tirar” (1140) means to pull or draw and the word s common to other romance languages. retirar dates to 1570