People may have different intuitions about the capability of the average person, but they're wrong. Not all opinions are equally valid.
Reality is one way, and we build models of it in our minds to differing degrees of accuracy - the better your models the better you are equipped to make decisions in life. This applies to political decisions, major life choices, what you eat for breakfast.
Politicians are not only not very well versed in the fields they need to understand, they're sometimes purposefully ignoring it in order to do something popular among their voters. Direct democracy makes this a bigger problem - it turns into tyranny of the majority and there is no check on what is popular (in Switzerland there are actually a lot of checks, but I'm talking more in general here about Athenian style direct democracy.)
Imagine a direct democracy in France once they have a majority Muslim population - you could start to watch the freedoms we take for granted in the West being rolled back one at a time. And it's not that their ideas are equally as good as our Western ideas - not all ideas are equal, and I think despite being obviously biased, it's true for me to say that many of our ideas are superior.
If you had a direct democracy in South Africa, they would take all property from the rich and redistribute it. The country would promptly fall apart like Venezuela and Zimbabawe where similar things happened. In Switzerland I think people understand the ramifications of doing, what on the surface, sounds like a good thing.
Representative democracy doesn't save us from this at all (the scenario in South Africa looked like it would come to pass, and they reversed course under international pressure) but it may curb some of the worst excesses of a direct democracy.