Not every reply would be a rebuttal. Not even every reply challenging the premises of the parent comment would be a rebuttal. Maybe "rebuttal" is the wrong word.
In a discussion being had in good faith, a thread will frequently go into a pseudo-debate mode to "find the truth" of a statement someone offered. Kind of like we're doing here. We all add anecdotes and counterfactuals and so forth, and see where the inductive process takes us. None of these comments would/should be tagged as rebuttals.
But there's a very specific situation where, I think, this feature is an important addition: when the original comment (or the post-link heading the discussion!) just doesn't know what it's talking about, and the reply outlines why this is so.
The concept is less like "this post disagrees with its parent, and so up-voting (agreeing) with it should mean down-voting (disagreeing) with its parent", and more like "this post is a petition to flag/retract its parent, and up-voting it is signing that petition."
This is why I had point 4 in the above, which might otherwise seem an unrelated feature: negatively-scored posts are not "disagreed with", but rather "flagged dead." But negatively-scored posts must still stay visible, in order to give requisite context to their positively-scored rebuttal-comments. And, in fact, a thread containing a negatively-scored top-comment might even still be the top-sorted thread, if its replies are considered valuable enough.
(One might still want to add some visual effect to remind those reading the post that the community considers it "retracted." Perhaps adding a strikethrough that disappears on hover, or a background of faint red Xes. You don't want to make the post illegible—it's still necessary context for its subthread, unlike the current HN/Reddit system where the post "fades" to nothing, and then the whole subthread gets considered a lost cause and collapsed.)