why can't we divide by zero ?! [duplicate]

By definition, for any $x,y$ in a field, $\frac{x}{y}$ is the unique field element $z$ (if it exists) such that $zy=x$. If $y=0$ and $x\ne 0,$ then no such $z$ exists. If $x=0$ and $y=0,$ then we don't have uniqueness.

That's why we don't/can't define division by $0$.

Now, if we expand the definition of a field to allow $0=1$, then it is proved easily that $0$ is the only element of the field--making such a field a supremely uninteresting structure.

You are correct that division by zero results in statements such as $1 = 2 = 3 =\cdots$, but that is not just a statement about facts in the real world (or "physical world"): mathematics as we know it would fall apart if this is allowed. What, after all, can be said, mathematically, if we have that $1 = 2 = 3 = \cdots$?

Just consider the implications, as they are vast, if we division by zero defined, and hence "meaningful"...

How would you define division if you allow division by zero? See, e.g., this answer regarding division by zero, with respect to how we define division, and division as we know it would fail if we were permit division by zero.

Indeed, how would we define $0^{-1}$ so that $0\cdot 0^{-1} = 1$?

These questions are simple prompts to suggest that to allow/define division by zero would entail having to redefine all axioms of arithmetic, and the field axioms, and much more. I.e., any successful redefining and reconstruction of a consistent system which is also consistent with allowing division by zero would yield, as first suggested in the comments, a system which would be exceedingly uninteresting, even perhaps meaningless.