X divided by Y means X number of elements equally distributed across Y number of groups. The result of division is not the number of elements that remain in the original, undivided, pool of elements but the number of elements in each one of the divisions.
31 divided by 0 means 31 elements equally distributed across 0 number of groups. How many elements do we get in every group after such an operation? But there are no groups – there are 0 groups – so we can’t really answer. Therefore, the result is undefined.
Ecmandu is speaking of a different operation – not division – and he does so because he thinks that words precede concepts rather than the other way around.
Division is not a subtractive operation. You do not remove elements from the starting pool of elements using certain method then count how many elements remain. That’s not division.
Similarly, multiplication is not an additive operation.
If our language implies it, then that’s the problem of language, and you shouldn’t confuse it for a mathematical problem.