1. You can make a rebuttal against/with the speaker.

Question

2. You can rebut against the speaker.
3. You can rebut the speaker.
4. You can rebut with the speaker.

(In a debate, which one can be used when a person make a counterargument. Thank you.)

Answer 1

I'd use 3 with a little rephrasing:

You can rebut the speaker's argument.