Why does $0/0$ have to be undefined?

Question

Why can't it no be $\pm$ Infinity?

If $x/1$ is $x$ then $x/0$ should be $\pm$ Infinity.

Answer 1

If x/y=z, z*y=x.
Agree?
For 0/0, we have z*0=0. z can be any number, thus 0/0 can be anything.