To most non-creationists it's pretty clear why creationism has no place in public schools, but here are the reasons, explained like you're five.
There are two basic reasons why creationism isn't taught in public schools.
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The first reason is that creationism is a religious belief. It says that the universe and all life on earth was created by God. But in America, one of our guiding concepts is separation of church and state, meaning that the government is not allowed to endorse religion—including in public schools, which are run by the government. Some creationists decided that they wanted to make their ideas look like they weren't religious, so they came up with intelligent design (ID).
ID says that the universe and all life on earth was created by some very powerful being, but doesn't speculate on what that being might be. But here's the problem: most of the major ID supporters are Christians who are trying to use it to promote Christianity. It's basically just religious creationism in disguise, which is exactly what a judge ruled in an important 2005 court case. But what if ID weren't being pushed for that reason? Then it wouldn't necessarily be religious, so could we teach it in schools?
That brings us to our second reason: even leaving the issue of religion aside, creationism (including ID) can't be taught because it isn't scientific. A scientific theory needs to be testable. It needs to make specific predictions about what we should expect to see if it were true, and it needs to be capable of being proven wrong if we don't see those things.
But without some details about this intelligent being—its traits and behavior—we have no way of predicting what kind of impact it would make on the world. And let's say we do make up a prediction: maybe a designer would create the best possible life forms. If this is proven wrong (say, by poor design), ID supporters can just say that maybe the designer behaved some other way instead. The "best" solution that supporters have come up with is probably specified complexity, but that's not saying much: it's a vague, deeply flawed attempt at telling apart designed and undesigned objects that has never actually been useful in practice.
So there we have it: creationism isn't taught because it's both religious and unscientific. Many people naively think that we should be "teach both sides" in the interest of "fairness," but that would be no more "fair" to students than teaching astrology in an astronomy class. Of course, the creationist movement could be mentioned as a historical footnote in a course on world religions or American politics, but that's a different matter. As far as the science classroom goes, it's been rejected twice over, and rightly so.