Actually, it’s pretty straightforward. It’s (with an apostrophe) is always a contraction of it is, never a possessive. So why is it so common to see that apostrophe where it doesn’t belong, in mistaken phrases such as “on it’s own”?
It’s quite understandable: That’s how the nouns do it. We’re so familiar with making a noun possessive by adding apostrophe + s that we don’t even think about it:
A chef’s knife
The King’s Speech
But that’s not how pronouns work in English. To make a pronoun possessive, we don’t add apostrophe + s; we use a different word:
It’s simply an unfortunate coincidence that the possessive form of it is made by adding an s without an apostrophe. So it can feel as though the apostrophe is “missing,” as indeed it would be in the case of a noun.
Just remember: Whose apostrophe is it? It’s never its apostrophe.