Why did the framers create repubilcan and democratic democracies instead of direct democracy?

"How" is easier to answer, but since you asked the "why" I'll try my best to explain why.

At the time of James Madison and in creating the Constitution for our Democracy we live in now, there was no way of knowing just how it would (230+ years old) translate to today's government. To quote Robert Dahl from "A Preface to Democracy" he begs the question whether or not Madison would have foreseen the problems that A Democracy has created for us (there are many, you can look them up). His answer: "I highly doubt it". They established a form of republican Democracy as the framework because (as explained thoroughly in The Federalist #10) a direct democracy creates, among many other things, tyranny of the majority.

So, to answer your question, we can only try and assess and analyze why. But, there are some facts and viewpoints that should be taken into consideration.