Why thank you for asking! You see, Philosoraptor, this can be solved mathematically.

The equation your reasoning uses is f(x) = y + xy, when f(x) is the original statement (either toasters don't toast toast or people don't kill people), x is the verb from the original statement (either to kill or to toast) and y is the noun from the original statement (either people or toast).

So, with the first set of input data, "guns don't kill people" produces an output of "people kill people". Then, the second set of data, "toasters don't toast toast" comes out as "toast toasts toast".

But, let's try a new equation. Like f(x) = p + xy. And in this equation, let's let p be the constant "people", keep f(x) as the original statement, keep x as the verb from the original statement, and keep y as the noun from the original statement.

Now, "guns don't kill people" has an output of "people kill people" as it did before, but "toasters don't toast toast" has an output of "people toast toast". A toaster is a tool that people use to toast toast, but nonetheless is still an inanimate object, and therefore does not toast toast on its own.

Philosoraptor obviously needed to have some julimagination there.