Counterexamples are simply the such examples for a given statement ,which meets it's requirement or all conditions to obtain a certain result, yet doesnot produce the same result, thus it contradicts its conclusion but at the same time satisfying it's
all necessary conditions .
The best example of it is Money makes a man happy
And it's counterexample is : Ram remains sad despite of rich lifestyle
So , the above example , fulfills the condition of being having lot of money by Ram but it contradicts it's result of being happy , as Ram is sad despite of all money ,. May be Ram has recently lost some dear or near one which made him sad about it