A strong counterclaim may:

A. Make arguments that are easy to refute

B. Change the subject to something more agreeable

C. Support the original claim.

D. Partly agree with and partly oppose the claim.

A. Make arguments that are easy to refute

It's important to understand the opposite side to your argument, but your counterclaim should be easily refuted by the rest of your argument, typically within the same paragraph. This shows that you've done your research on both sides, but still your side is much more strongly supported.