Truth be told, there is no real antagonist in the story. Since the narrator is omniscient, we are granted access to a wide variety of points of view. A few characters are made to seem ridiculous (Sitnikov, Madame Kukshin), but there are no villains in Fathers and Sons. It's almost as if Turgenev's rule of thumb for creating a character is that he has to be able to sympathize with him or her. Hence the reader might just as easily prefer Pavel Petrovich to the arrogant young Bazarov. Yet we call Pavel Petrovich the antagonist because he is at odds with Bazarov. They do, after all, have a duel, even if the end is less than catastrophic.