Why is a short-run aggregate supply curve upward sloping?

Because it reflects the marginal cost of the company. There will be supply only when the marginal cost is greater than the average cost.

By the way, the short-run aggregate demand is an upward slope for firms in perfectly competitive markets. Note that!

So, as I was saying, in perfect competition there is the assumption of zero economic profit - no agent profits more or less than any other. That is because firms can only charge customers their marginal cost of producing; it means, therefore, that price = marginal cost.

Source: Pyndick and Rubinfeld (2014).