The reason is this.
ba is
defined to be the unique number
c such that
cb=a.
The key thing to note here in this definition is that there is an assumption. It assumes that this 'unique number
c' exists.
Let's try to find
0a where
a is nonzero. It's the unique number
c (if it exists) such that
c×0=a. But it is axiomatic that
c×0=0, so we need the unique number
c such that
0=a. But
a is nonzero, so there does not exist such a number
c and so
0a doesn't actually have a definition. It doesn't exist. If we are trying to assign a value to
0a by our original definition of division then we are making a false assumption (namely that
c exists).
What's interesting to note is the case
a=0. Then we require the unique number
c (if it exists) such that
c×0=0. But this is true for any
c, so c is not
unique and so
00 is undefined as well (this time for contradicting the latter part of 'exists a unique number
c).'
In fact we call the expression
00 indeterminate, since any
c satisfies the required equation
c×0=0.