If you divide something 12 feet long into 3 parts, you don't get 4 parts, you get 3 parts that are each 4 feet long. So, if dividing a number by 0 yields infinity, you would expect that dividing something physical into 0 parts would yield 0 parts, each of infinite size, whatever that means.
It's fine to be pedantic in math. You can't divide something 0 times, there's no solution for that. You can divide something by infinite times, but infinity is not 0. This might help explain things:
Sorry to be pedantic.