I think women make good snipers. There have been more than a few.
Old men and women can both have the shooting capability of a sniper, but can they fulfill all the physical challenges that an American sniper may face to conduct a mission?
My wife is a CC instructor, pretty good in math, and a pretty good shot overall. However, she has trouble understanding the finer points behind the mechanics and detail of accurately lobbing bullets long distances. In her words: "This is a lot of trouble just to make one shot."
I offer WWII Red Army snipers as proof. Not to mention the female fighter pilots of same.