I'm not great with English and all so sorry in advance,
rebuttal: When two people debate, one of them makes an argument, and the other follows with a rebuttal, which, plainly put, is the "no, you're wrong and this is why" argument. So you'd need solid evidence to back up your claim
Counterclaim
the four parts of an argument: claims, counterclaims, reasons, and evidence. A claim is the main argument. A counterclaim is the opposite of the argument, or the opposing argument. A reason tells why the claim is made and is supported by the evidence.
Sorry I would have a better understanding of it if it wasn't midnight where I am. Im is probably no help ... sorry