Buying flights separately instead of together is cheaper. Why?

I'm on the American Airlines website looking at flights. I'm looking to fly to from Nashville to Brazil this July (Jul 18 - Aug 4). If I buy a flight to Miami ($200ish), and then buy a separate flight to Manaus from Miami ($500ish) I get a total of $700 dollars. But if I fly staright from Nashville to Brazil with a stop in Miami, its $1300 dollars. Why is this?