The worst part is that they are both, in a critical sense, wrong. There is no absolute 100% universal "right" answer to how division works—it's just a matter of convention! Merely getting into the argument of whether 1/0 "is" 0 is wrong.
There are practical reasons why we leave division by 0 undefined in "normal" arithmetic but we could, just as easily, operate in a world where 1/0 is defined. In some contexts, 1/0 = 0 is a totally sensible convention! In others, we can define it to be ∞ or, hell, something else entirely.
This approach of teaching math as a bunch of universal facts that are either true or false is actively harmful—but super convenient for top-down education and assessment!—because it teaches people the wrong way to think about math or even about conceptual models in general.
There are practical reasons why we leave division by 0 undefined in "normal" arithmetic but we could, just as easily, operate in a world where 1/0 is defined. In some contexts, 1/0 = 0 is a totally sensible convention! In others, we can define it to be ∞ or, hell, something else entirely.
This approach of teaching math as a bunch of universal facts that are either true or false is actively harmful—but super convenient for top-down education and assessment!—because it teaches people the wrong way to think about math or even about conceptual models in general.