Please read: But we don’t learn anything that way. We arrogantio’s have either learned to tone it down, or, if we have failed to learn that important lesson, we have learned something else out of sheer selfdefence, and that is just to filter out the irritated glances others throw us.
In college, there was girl in our department who considered herself hot shit. She is a semi-famous singer here in Korea, and she’s spent some time abroad, so she always considered herself the most attractive girl on campus as well as the smartest. She wasn’t stupid, but she definitely was not the genius she fancied herself to be. I always enjoyed her presentations, though. I would ask her question after question until her whole flimsy argument fell apart. Much more effective than rolling my eyes at her. You could try that approach. Or you could try a nicer approach per the suggestions in this thread, which would probably be the decent thing to do, if not as much fun. 
WORD !!
I’d just sit up front when they’re giving their speech and then just be the worst possible listener. Stare out the window, look at your watch a lot, yawn.
If asked to comment on what he said just reply “Oh, sorry, I wasn’t really paying attention.”
I agree with HazelNutCoffee. You can attack the argument if you want to go through the trouble. Hopefully, it will be a nice humbling experience for the idiot student. Just remember: Don’t get into a pissing contest with someone with a bigger bladder than you have, as a Bible professor I know of is apt to saying.
If it is was in any other class, I would say possibly the best route would be to ignore it but public speaking is a nightmare in itself and no one needs to have some rude little snot acting up. It needs to be brought to the attention of the professor as part of public speaking is not only learning how to speak but also how to act during a talk. Do it after class, in the prof’s office, etc so as not to draw undue attention as the “snitch”. (Actually, most of the class will probably be grateful) In my four and a half years of college, I have done this twice. If you can, get a couple of others to go to the prof with you…power in numbers. Both times, in my case, the situation was dealt with very quickly.
I am pretty non competitive. I like peace and happiness, not bloodshed. In my undergrad years, I would have people who would play those silly games trying to pull me into competition crap. (FTR, I graduated with a 3.67gpa, was a member of student govt, honors program and associations, etc…yeah, a real good two shoes). I hated it! I really feel this is what this person is doing. He feels you are threat and is trying to pull you down to his level.
I will have one rule when I am a professor: If I see any bad attitudes (eye rolling, loud obnoxious sighs, etc), I will stand that person up and verbally quiz them. Let’s see how much they know.
If all else fails: This too shall end.