A counterclaim is.

a claim that includes a true statement.

an argument made against a claim.

an examination of a claim.

evidence used against a claim

A counterclaim is an argument made against a claim because the meaning of counter means against like if someone says democrats rule another may say republicans are better, that's their view against yours so that's why its important to have a claim for a counterclaim, basically a reason why your statement is right. * The example of the politics is not used to offend any democrats or republicans but rather its used as a teaching example.