Rebut
Etymology
From Old French "rebuter" (to thrust back, repulse) — "re-" (back) plus "boter" (to push, to strike, to butt), the same "butt" as a ram butting with its head. To rebut is to push back against an argument; it is a move in the exchange, not a verdict on it.
verb · /rih-BUT/
To argue against a claim by offering opposing reasons or evidence.
What it names
Use it for mounting a counter-case — presenting a reply meant to weaken an argument, whether or not it ultimately wins.
Example
The defense rebutted each charge in turn, though the jury wasn’t persuaded.
Related idea
The key contrast is with refute: to rebut is to argue against a claim; to refute is to actually prove it false. A rebuttal is an attempt, a refutation is a success — you can rebut something and lose the argument, but you cannot refute it and be wrong.