Dividing by zero makes any number equal to any other number. It renders the number system meaningless.
Suppose a=b:
a^2-b^2 = a^2-ab = a(a-b),
but
a^2-b^2 = (a+b)(a-b);
therefore,
a(a-b) = (a+b)(a-b)
and dividing by a-b we have
a = a+b.
Let a = 1. Then 1 = 1+1 = 2.
Isn't that special?
Yours is the proof that satisfies!
Similarly, in truth-functional calculus, allowing both p and not-p permits the generation of limitless propositions.
Once one accepts a lie as truth, one can believe anything at all without evidence at all. The socialists teach us that.