Acceleration occurs despite equal and opposite forces because these forces act on different objects. In the case of a horse pulling a wagon, the horse exerts a force on the wagon, while the wagon exerts an equal force back on the horse. The net force on the wagon is the horse's pull minus friction, allowing it to accelerate. Similarly, the horse experiences a greater frictional force with the ground, enabling it to accelerate forward as well. Understanding that net forces, not just equal and opposite forces, determine acceleration is key to this concept.