It is not recommended to wear conventional sport shoes for climbing. Whether you are climbing indoors or outdoors, the rubber on the bottom of the shoe is what will give you a firm grip on the wall. The rubber of a normal athletic shoe will be slippery and far less durable than the rubber of a climbing shoe. You'll only end up damaging your footwear. Also, the very precise shape and fit of climbing shoes are designed to allow climbers to feel the holds of the wall under their feet, which is not the case with ordinary shoes.