Why do firms only make normal profit in a perfectly competitive market?

Under a perfectly competitive market, there are a large number of buyers and sellers, where each of them are price-takers. If we imagine a supply and demand diagram, the S=D at equilbrium. If firms are initially making supernormal profit, then other firms will have an incentive to join the market. The market supply curve will shift rightwards.

If we now consider an individual firm's supply curve, it will be highly elastic because of all other firms selling identical products. The firm's supply curve will shift downwards as a result of a fall in the market price. New firms will carry on entering the market until AR=AC and firms are only making normal profit. After that, no firm will have an incentive to join because businesses will be earning the bare minimum needed to survive in the market.