The problem is that the rules of English are backwards here.
John's = it belongs to John. it's != it belongs to "it".
Why that is, I don't know, but it's true. I assume it's to distinguish from "it is" and "belongs to it" because you don't have the same problem with "John is" being "John's".
An easy way to remember is that "his" and "her" don't have apostrophes either, just like "its".