The logic is based on the idea that right-handed combatants will find it hard to wield their weapon effectively fighting their way up a clockwise staircase as t

The logic is based on the idea that right-handed combatants will find it hard to wield their weapon effectively fighting their way up a clockwise staircase as the central column will get in the way, whereas those fighting down the staircase will have plenty of room near the outer wall/bannister to wield theirs. Conversely, an anti-clockwise staircase will give an advantage to right-handed combatants fighting up, and an impediment to those fighting down. Therefore, given that the majority of people are right-handed (and lefties are often taught to fight right-handed anyway), and the idea that if an attacker manages to enter a castle they will then be fighting their way up the stairs against defenders above, clockwise staircases give an advantage to the people tasked with defending them.