Some of the things that to me would damage the barrels.
Cleaning from the muzzle end, and not using any type of guide so that the rod is rubbing against the crown.
Using copper solvents that are ammonia based, and leaving them in too long so it etches the steel.
Using the stainless steel brushes.
Scrubbing the bore with dirty patches.
An oversized rod that is constantly rubbing against the rifling.
Pusing with an undersized, or flimsy rod so that it flexes and rubs against the rifling.