counterexample.
One way to show that a statement is NOT a good definition is to find a counterexample. In description, counterexample is an exception to a “proposed general rule or law”. Philosophically, counterexample somehow generalizes a set of ideas or a notion declared in its position. For example, all colors are white. Therefore it is wrong to say that red, orange, blue or any other “color” is not a color by which the statement declared itself.
Moreover, in mathematics counterexamples are utilized frequently to testify theorems' limitations.