A counterclaim is a claim rebutting or opposing a first claim made. It introduces reasoning behind the argument, and evidence that support it. Claims and Counterclaims can be found in essays, scientific documents, argumentative writing, debates, and litigation.
This type of argumentation is possible whenever there are two or more different ideas or opinions over an issue, and both parties have evidence to prove what they are saying. For example, in a lawsuit over a car accident, an essay over theories of evolution and creation, a debate over two political ideologies, etc.