Assertion: Earth has an atmosphere but the moon does not.
Reason: Moon is small in comparison to earth
 

Earth has an atmosphere but the moon doesn't. Thus the assertion is correct. Also the moon is very small in comparision to earth. So the statement under reason is also correct, but, the reason is not the correct explaination to the assertion. Infact the correct explaination is that due to smaller size, the moon has less gravity than earth and so it can not hold the gases like earth and thus no atmosphere in it unlike earth.