Why does the order of operations matter in math?

Order of operations matters because notation needs one shared meaning. For example: $$2+3\cdot 4$$ could mean either: $$(2+3)\cdot 4=20$$ or: $$2+(3\cdot 4)=14.$$ If everyone chose their own order, the same written expression would not communicate one value. Multiplication comes before addition because multiplication is repeated addition and tends to bind more tightly in algebraic structure. For example: $$2x+3$$ normally means "two copies of $x$, then add 3," not "$2$ times $(x+3)$." Parentheses override the convention: $$(2+3)\cdot 4.$$ So PEMDAS/BODMAS is not a law of nature. It is a convention that keeps mathematical writing unambiguous. The deeper rule is: if there is any chance of confusion, use parentheses or a fraction bar.