Summer flooding washes out stretches of fence, but the cattle themselves cause a great deal of damage. Like most caged creatures, cattle instinctively probe for weak spots in the cage and break out when possible. Cows also love to rub on posts, and so will occasionally push a favorite back-scratcher right over, breaking and stretching wire. They will also deliberately break through if they are thirsty and a water source beckons. And even when they can't manage to get through a fence, they will make mess of it trying.
Bulls can cause more thorough damage.
Natural selection ignores barbed wire, so it is not unusual for two bulls in adjoining ranges to fight for dominance right through the fence. Once, while helping vaccinate some cattle I saw two bulls ruin a fence. We had driven these bulls to the corrals along with about thirty cows, most of which had calves tagging along. After vaccinating the bulls, we turned them out into a larger holding pen, and started running the cows and calves through the chutes. My highly-specialized job was to put a green mark on the hip of each animal with a chunk of greasy chalk to show that they had their shots.