Why do firms in perfect competition earn normal profit in the long run

In the long run, all factors of production are variable. Also, two of the assumptions of firms in perfect competition are free entry and exit, as well as perfect resource mobility.

In the long run, firms making abnormal profit will attract new firms, which will enter freely due to the two assumptions already stated. This would increase the industry supply (and shift the supply curve to the right) which will decrease the industry price.

New firms will stop entering the market once existing firms make zero economic profit.

On the other side, in the long run, firms making losses (producing under the break-even price) will exit the market due to not being able to compete with other firms, which will decrease industry supply (and shift the supply curve to the left), which will increase the industry price.

Firms will exit until the remaining ones make normal profit again.

So in the long run, all firms in perfect competition earn normal profit (or zero economic profit).