Synonyms of counterargument may include rebuttal, reply, counterstatement, counterreason, comeback and response.
An attempt to rebut an argument may involve generating a counterargument, or finding a counterexample.
This form of counterargument — invented by the presocratic philosopher Parmenides – is commonly referred to as a retroactive refutation.
[3] In a debate or in speaking contextual evidence, a counterargument can be handled in a variety of ways.
You may concede it, minimise it, dismiss it as irrelevant, or attack the supporting evidence or underlying premise.