Women can count to twelve if they want to ...

But shouldn't women be able to count to twelve?

Maybe with a mirror....
Order of operations is a convention that people agreed to use at some time.
Yes, in a sense. It's not a convention like grammer though that can change with time. Math as we know it does not exist without order of operations...
Left to right parsing is not as crazy as it seems....
As I posted above, you do solve from left to right with mathematical equations because multiplication is interchangeable with division just as addition is interchangeable with subtraction. You don't dive into the middle of an equation to solve all of the addition before solving all of the subtraction. You solve them from left to right after PEMD has been satisfied. This is something you see all the time right after people learn PEMDAS... they make a mess of the equation trying to stick with that order.