The friction between cytoskeletal filaments is of central importance for the formation of cellular structures such as the mitotic spindle . This friction is caused by passive crosslinkers, . Here, we use theory and computer simulations to study the friction between two filaments that are crosslinked by passive proteins, which can hop between discrete binding sites while physically excluding each other. The simulations reveal that filaments move via rare discrete jumps, which are associated with free-energy barrier crossings. We identify the reaction coordinate that governs the relative microtubule movement and derive an exact analytical expression for the free-energy barrier and the friction coefficient. Our analysis not only elucidates the molecular mechanism underlying crosslinker-induced filament friction, but also predicts that the friction coefficient scales superexponentially with the density of crosslinkers.