So, Person2 acknowledges the importance of Person1's work but then publicly passes judgment on the manner in which they presented it as a way of dismissing Pers

So, Person2 acknowledges the importance of Person1's work but then publicly passes judgment on the manner in which they presented it as a way of dismissing Person1's main point. Person1's behavior would be widely ridiculed and probably booed if this happened at a conference. The more professional approach is to simply present one's case without commenting on the quality, style, or manner of the other's presentation. My two cents, best of luck in your studies :)