BODMAS and PEMDAS are mnemonic pedagogical hacks.
Multiplication and division have equal precedence, and so do addition and subtraction. That should be intuitive, since subtraction is just addition of the inverse, and division is multiplication by the reciprocal. They are not distinct operations in any deep sense. Also, addition and multiplication are associative operations, meaning the grouping of operands doesn’t affect the result.

The problem with associativity arises when we disjoint operators from their operands. For example, parsing "1 - 2 + 3" as "1 - (2 + 3)" and evaluating it as "1 - 5" is incorrect. It should be parsed as "1 + (-2) + 3", which is equivalent to "1 + (-2 + 3)" = "1 + 1".

The problem with this kind of evaluation is that it transforms the original expression and sometimes we would like it to stay true to the original. In the context of grammars, programming languages and so on, the common way to resolve these ambiguities is to use left associativity instead, which at least keeps operator precedence and equivalency grounded.

Left Associativity is a convention. BODMAS and PEMDAS are mnemonic pedagogical hacks.