Is it fair to apply logical analysis to relativistic principles?

Many relativists say no, but I do not see why not. If a relativist were to convince me that logic isn’t necessary in examining relativism, he’d have to convince me using logic, which would be self-defeating. If a relativist uses relativism -- the subjective view of his own opinions -- to validate his position, he is using circular reasoning; namely, he is using relativism to establish relativism. So, either way he has lost the argument.