When thinking of the beginnings of the NRA, it helps to visualize Elmer Fudd. Yes, THAT Elmer Fudd, the hapless hunter from the Bugs Bunny cartoons. He's not a very good shot, and the same affliction for real hunters and shooters played a part in the formation of what was then called the National Rifle Association.
It wanted people to shoot better when they fired guns, and to understand gun safety. It's only in recent years that the NRA became such a fierce defender of gun ownership at really all costs.
Investigative journalist Frank Smyth runs from the beginning to the now in his book The NRA: The Unauthorized History. We revisit the author's visit from 2020 here.