For snipers, Quickscoping is really just the evolution of sniping in general. A person plays a sniper because they enjoy pulling off that accurate shot. As a sniper improves skill wise, they begin to be able to scope in faster and faster. Most snipers realize that staying scoped in (hardscoping) is actually a bad thing. Its actually wiser to wait until a target is spotted, track them before you scope in and then scope in. The reason is simple, its faster and more efficient. And because we have the ability to scope in and kill quickly, then it becomes a choice, Do i stay here? or do I go to where the action is and help my team more?
Furthermore its the logical thing to do, as a player some of us try to push ourselves to do better, pull off that shot quicker. So if you can already see an enemy, scope in and kill them quickly, why wouldnt you begin to move around?
EDIT: Just wanted to say ZRXD, Thanks for being civil.