Counterexample is an example with a negative connotation. Whereas an example may be used to support or illustrate a claim, a counterexample is used to refute an assertion.
Statement: All whole numbers are even.
Counterexample: Consider numbers 3, 5, 7, 9, 11, 13, 15, 17, 19, 21,.... These numbers are whole numbers, but not even numbers.
You give an example of whole numbers that are not necessarily even.