It means the opposite viewpoint. For example if I wrote a paper in favor of the death penalty, someone else could write the rebuttal against the death penalty.

Most rebuttals here start with name calling, have a lot of name calling in the body, and end with some more name calling.

A good essay presents a logical case, supplies clear evidence, cites specific incidents, and takes issue with others.  There is no standard format, but clarity is the one and only essential.

1. Proposal.  We propose a case, and state our argument for it.
2. Reply.  What will the opposition (if any) say in answer?
3. Argument.  We reply to the arguments that supposedly contradict our Proposal.
4. Rebuttal.  We reply to the argument, concluding the case with a call to action.

Readers will evaluate your work independently.  If you failed to find flaws in your logical case, they will find them and let you know about it.

Some of the most convincing I have ever seen are:

“Why I left atheism,” Allen Watson, 2012.

“Islam in our community,” James Holder, 2013.

“Mathematical proofs of Divine Creation,” Hal Bennington, 2012.

Persuasive essays are generally those essays which are written to persuade a reader about something, or a certain happening.