The old story that goes with standard gauge is that it was literally the width of two horses butts, the wheel-to-wheel distance of the standard two-horse Roman chariots and carts in use in Britain. Since carts were made by the people, using "story sticks", i..e., strips of wood with pre-marked measurements, this became standard throughout first the Roman Empire in Britain, and later Britain itself.
The centuries of usage had worn ruts in the Roman roads, and it was convenient to maintain the wheel spacing, which didn't change until better roads and railroads came along, at which point the cart and wagon makers were the only people with the skills to make coaches, for which they used the "standard" wheel spacing in place since Romans times - four feet 8 1/2 inches, the width of those two horses' butts in Roman times.
Narrow gauge rail is easy to understand against the perspective of the Continental Divide which stretches across America from North to South. The three foot narrow gauge meant less grading and blasting, smaller tunnels, tighter curves through the mountains, lighter rail, lighter bridges and and it could be laid faster and more cheaply that standard gauge, which would have been prohibitive to build and operate in the mountains and narrow, twisting valleys.