Math is a language; written equations are like sentences.

"The man bit the dog" is just as valid as "The dog bit the man", but since we agree on the grammatical rules that when a Verb takes two cases the Object goes after it, which is "correct" depends on whoever the was bitten. If the man was bitten, the first one is incorrect and the second one is correct.

PEMDAS is the grammar of the equation. It's "correct" because it helps to all agree on what we mean. It clears up ambiguity.