With the possible exception of Ovid, Aristophanes more than any ancient writer reminds us that people in the Long Ago were also human. Partly he manages this by putting absurd and ridiculous words in the mouths of Great Men instead of the somber speeches devised by his brooding contemporaries. Partly it's the way he pokes Greek society in the ribs and winks, letting us in on the Big Joke.
Mostly it's the way his jokes are still hilarious. We're not just talking giggle-worthy; Aristophanes' humor is only adequately appreciated with guffaws, the kind that force actors to pause onstage until there's enough silence to accommodate his delivery. Which begs the question—why aren't Aristophanes' plays produced anymore? They were intended to be acted rather than read, but for the most part they're relegated to the Dusty Section of the public library.
Perhaps the humor is too intelligent for modern audiences. Maybe it's too bawdy for those accustomed to highbrow art and whose conservatism is bound up with their love of classicism. Possibly the powers-that-be who fund theaters see too much of themselves in the satirized characters and feel the need to suppress such imagery.
Probably it's all these reasons and more. The Birds is not, after all, about the nonsense of divinity but the nonsense of human rulers. Lysistrata shows both the stupidity of men and the stupidity of war....and the animal instincts which motivate both. The Clouds shows us how we take some ideas too seriously and others not seriously enough, primarily by showing us that humans are not a breed to be taken altogether seriously. The Frogs is just plain funny.
Don't be shocked if Aristophanes crosses too many lines. Some of his jokes are crass, others irreverent, others bizarre, still others cruel. As a true satirist these were his weapons and his tools for showing people what they really look like. Sometimes the reflection we see is ugly, sometimes it's just a little more silly than we can bear, usually it's perfectly accurate. Which is about the best definition of humor, and the one Aristophanes mastered better than any writer ever.