This is only true if your system does not define division by zero. For example, taking the square root of a number that is not a perfect square is impossible in the rationals, making those numbers different from other numbers. You claim we should then take these so-called "numbers" out of the system, instead of finding a meaningful extension of our system. The latter choice brings new vistas of mathematics, while the former choice is a step backwards. Your personal problem with zero is echoed by others' problems with other aspects of other systems. Some may not want any numbers other than 1, because it makes no sense to define a new number other than a whole object. You may argue against this, but I'm sure you can see that your arguments will be just as futile as ours are to your belief.