Or so you thought. The sooner you realize it, the better off you'll be. It's is a contraction for it is or it has . That agrees with the rules. It is a pronoun , whose possessive forms never take an apostrophe.
Pronouns are special types of words.
Their genitive cases don't use apostrophes. Some, such as the their above, don't even add an s to form the possessive. Pronouns have special genitive cases, all lacking apostrophes. Okay, I cheated.