Because it has the unfortunate consequence of eliminating the uniqueness property of fields. If you allow 0 to have a multiplicative inverse 1/0, then the prod

Because it has the unfortunate consequence of eliminating the uniqueness property of fields. If you allow 0 to have a multiplicative inverse 1/0, then the product of 0 and 1/0 must be equal to the multiplicative identity, which is 1. Then it follows that 0 = 0 * 0 = 1. From here it's straightforward to prove that x = y for all x, y in the field F. A multiplicative inverse is a division. You cannot define division by x in fields without defining multiplication by 1/x and vice versa. The article is plainly incorrect in its attempt to refute this point (and in any case, shouldn't be using field theory to justify its purpose in the first place).