The purpose of presenting a counterclaim is to present a fair argument that does not choose sides.
address any objections to your claim and explain how they fall short.
show both sides of an argument, letting readers make an informed decision.
validate any objections to the claim being made.

The purpose of presenting a counterclaim is to validate any objections to the claim being made.

Explanation:

A counterclaim is a claim that rebuts a previous claim.

To rebut is to claim or prove that something is false.

So rebutting a previous claim in which one is trying to prove that something is false, is simply trying to make your objections valid.

When making a counterclaim, you're trying to show or prove that what someone else said is untrue or false and the main purpose of making a counterclaim is to show your objections to the previous claim and validate it (that is showing that it is valid).