In American football, why is it called a "down" instead of a chance, or try, or attempt?

In American and Canadian football, a down refers to a period in which a play transpires.
https://en.wikipedia.org/wiki/Down_%28American_football%29

American football resulted from several major divergences from rugby football, most notably the rule changes instituted by Walter Camp, considered the "Father of American Football". Among these important changes were the introduction of the line of scrimmage and of down-and-distance rules. In the late 19th and early 20th centuries, game play developments by college coaches such as Eddie Cochems, Amos Alonzo Stagg, Knute Rockne, and Glenn "Pop" Warner helped take advantage of the newly introduced forward pass.
https://en.wikipedia.org/wiki/American_football#History

Down is also an adjective to describe the condition of the player with possession of the ball after he has been tackled or is otherwise unable to advance the ball further on account of the play having ended (e.g., "He is down at the 34 yard line").

https://en.wikipedia.org/wiki/Down_(American_football)#Description

'n the early 19th Century in rugby football, the ball became dead in the field of play only by mutual consent of opponents. A player carrying the ball and held by opponents would say, "Held!", and his opponent would say, "Have it down." That is, the ballcarrier would declare himself fairly held, unable to advance, and an opponent would call on him to put the ball down, initiating the scrimmage. In modern rugby league, this is called a tackle and each team has six tackles to score; if they fail then possession changes over to the other team.

In American football, the concept of the act of having the ball down gave rise to "down" as the condition of the player so obligated, and the ball carrier could call for a "down" voluntarily. Although NCAA rules have effectively abolished this (as the ball carrier dropping to the ground immediately ends the play), other codes for North American football, such as the NFL, still allow (as one way for the ball to become dead) for the runner to cry "down".

Eventually the rules officially applied the word to include all of the action from the time the ball was put into play (whether by snap or free kick) until it became dead.'

https://en.wikipedia.org/wiki/Down_%28American_football%29#Derivation