Why do single firms in perfectly competitive markets face horizontal demand curves?

Because increasing price will cause the demand to become zero.

Explanation:

In a perfectly competitive market, there is a large number of buyers and sellers. Such that no single buyer or seller can affect the market price. There is no restriction on entry and exit of firms and perfect knowledge is freely available.

The sellers in this market sell homogenous products, so if a seller charges a higher price, the buyers will instead buy from its rivals. And if the firm reduces its price it will face losses. So the individual demand curve of a firm or supplier is a horizontal line on the level of market equilibrium price.