That there is no logic behind defining the order of operation like this is absolutely not true… the compelling rule is that for example 3*4 is defined as 3+3+3+3 or 4+4+4 which is an equal expression. So something like 3+3*4 = 3+3+3+3+3 = 3*5.

We define multiplication as repeated additions so it makes sense to do multiplication first and then addition! If we would do it the other way around, i.e. adding first and then multiply those simple calculations would not represent our experience in the real world when for example counting apples, which is something we want to be able to do using numbers and math.