I would never move anything back and forth in the barrel. Cleaning swabs, snakes, etc should only travel the same direction as the bullet.
I pretty much addressed this in my other post. I have been shooting & cleaning since 1948. Never seen a bore hurt by back & forth motion yet. This includes scrubbing M1 rifles using back & forth and hot lye soap water. A barrel is dirty after just one round fired. Shooting ammo through that barrel at high velocity with high temperature is a lot worse than scrubbing with a bore brush wet with bore cleaner or soap.
I would like to see some evidence of this obsurd statement
Me too.