Simple answer: because that's the way English works.

I am     -> I'm      ||  I have     -> I've
You are  -> You're   ||  You have   -> You've
He is    -> He's     ||  He has     -> He's
She is   -> She's    ||  She has    -> She's
It is    -> It's     ||  It has     -> It's
We are   -> We're    ||  We have    -> We've
They are -> They're  ||  They have  -> They've

There is a certain amount of ambiguitity here, but the precise meaning can usually be determined by context. You'll notice that the same ambiguity exists with he and it is/has.

Furthermore, it's (it is / it has) can also be confused with the possessive its (note no apostrophe)!

There are no contractions (that I'm aware of) for was (the past tense). She was is always She was, but She had can be contracted to She'd.

‘An A-Z of English Grammar and Usage’ by Leech and others suggests the following:

With be, use the contraction + not (e.g. That’s not right).

With have and modal auxiliaries, use the verb + n’t option, e.g. hasn’t, can’t.

The authors go on to say that forms such as She isn’t hungry, as opposed to She’s not hungry, are less common, and that forms such as I’ve not met him, as opposed to I haven’t met him, are much less common.

The authors don’t say on what basis they make their recommendations, but they are likely to be based on frequency of use. There doesn’t seem to be any difference of meaning or emphasis. I would just add myself that a contraction such as I’ve not met him sounds more formal, perhaps because of its lower frequency.