Why did the framers of the Constitution decide against a system that directly elected the president by popular vote?

Framers had their blind spots. I won't mention slavery for the moment, since that's where everyone goes and since that blot has been amended out of the Constitution (and since many of the Framers, notably Ben Franklin and Alexander Hamilton, were anti-slavery).

One of the big blind spots, which seriously interfered with their thinking on many constitutional matters, is that they believed it would be possible to have national politics without political parties. This played a big role in the creation of the Electoral College system. The strange tale of how the electoral system came about puts some of its weird features into context. Once you get this context, it is at least understandable what the Framers thought they were doing.