Arkady often speaks of how much Bazarov means to him, how much he has learned from Bazarov. Rarely do we hear Bazarov say anything complimentary about Arkady. He should. From the start, Arkady functions like the perfect public relations manager for Bazarov. He tells his father that Bazarov "knows everything," and later tries to defend his friend's nihilistic position (3.15). Later, in town, Arkady shoots himself in the foot with Anna Sergeyevna because he spends all of his time telling her how amazing Bazarov is; she ends up becoming more interested in Arkady's friend than in Arkady. In short, without impressionable young men like Arkady around, Bazarov would have trouble ingratiating himself with anyone.
It's important to remember that this winter spent at university in Petersburg was the first time that Arkady had actually been out on his own. Nikolai used to make a point of accompanying his son to university and attempting to oversee both his studies and his friendships. In general, it's clear that Nikolai has been over-protective; now that Arkady is out on his own, it's no surprise that he is prone to fall under the influence of a stronger personality.
At the start of the novel, Arkady seems a little childish, but also more intelligent than he knows. His definition of nihilism is actually better than Bazarov's own. Arkady tells Pavel, "A nihilist is a person who does not take any principle for granted, however much that principle may be revered" (5.57). Of course, Pavel sees through Arkady's definition, but it's much more compelling than Bazarov's explanation that nihilists are those who renounce everything because that is what is most useful. The narrator also notes that when Arkady and Bazarov go walking, Arkady tends to lose the arguments although he is "more eloquent than his companion" (10.2). Arkady lacks nothing in intelligence, only in strength of will and cunning. One gets the sense that Bazarov bests him simply by telling him that he is wrong.
In this way, Arkady is very much his father's son. The arguments between Pavel and Nikolai are echoed in those between Bazarov and Arkady. Arkady, like his father, is a reasonable man, but he is also meeker than he needs to be. He tries to stick up to Bazarov when Bazarov bashes his family for being gentrified and old-fashioned. Yet Bazarov always insists on having the last word, and Arkady is not confident enough to keep him from having it. When Nikolai overhears them arguing, he waits for his son to stick up for him, but the conversation ends and "Arkady made no reply" (10.7). His father thinks this is a sign that Arkady agrees with Bazarov, but the truth is that Arkady's silence is what binds him to his father; they both give in too easily to the people around them.
Late in the novel, Arkady tells Katya that she is the one who has brought him out from under Bazarov's influence. We would argue that Arkady actually begins to develop a sense of independence earlier – when he meets Victor Sitnikov. Sitnikov also proclaims himself a disciple of Bazarov, and one might think that he and Arkady thus have something in common. Yet Sitnikov is like Arkady in a dark mirror. Arkady quickly perceives what a fool he is, and he can see how Sitnikov stupidly agrees with everything Bazarov says. Later in the story, Bazarov tells Arkady that the Sitnikovs of the world are necessary, and "only then in a flash did all the fathomless depths of Bazarov's conceit dawn upon him" (19.37). It is through Sitnikov that Arkady begins to understand how Bazarov belittles him, and when he realizes how little esteem Bazarov has for him, he develops the confidence to begin shaping his own life.
Early on in the story, we get a sense that Arkady is a kind and good son, even if he is, in his way, rebelling against his father. The first night he is home he prays for all the people around him, but "For himself he said no prayer" (4.35). Never mind the fact that he is posing as a nihilist, someone who doesn't believe in anything; nothing could be further from Bazarov's way of thinking than Arkady's selflessness.
The one moment when Arkady seems to feel superior to his father is itself mixed with empathy. His father is embarrassed about his relationship with Fenichka, and Arkady repeatedly emphasizes that he is perfectly alright with it. Arkady is self-aware enough to realize that one reason he takes pleasure condoning the relationship is that it is a sign that he has more advanced social views than his father. As he assures Nikolai, "he realized that he was delivering something like a lecture" (5.26). Yet the dominant feeling here is empathy for his father's situation. Arkady notices his own condescending tone, and does his best to control it. It's hard to imagine either Pavel or Bazarov worrying about the "tone" in which they put others down.
Through Katya, Arkady comes out from under Bazarov's influence. Katya explains to him how he is different from his friend; Bazarov is "a wild beast, while you and I are domestic animals" (25.20). Arkady is offended. Most men don't want to hear themselves described as a "domestic animal." Especially when the alternative is a "wild beast." Yet all that Katya is pointing out is that Arkady is a kind man, one who can find fulfillment in love and the quiet life. The biggest differences between Arkady and Bazarov are not those of philosophy, but of personality. There is a certain intensity to Bazarov – a mixture of pride, ambition, and meanness – that Arkady lacks. As Bazarov himself puts it (in characteristically intense terms), "There's no audacity in you, no venom" (26.150).
Explaining away Arkady's choice for the happy life, Bazarov compares him to a jackdaw, a bird given to pair bonding. It's not hard to perceive, though, that Bazarov is jealous of Arkady. Through Katya, Arkady has found what Bazarov hoped to find through Anna Sergeyevna, even if he couldn't admit it. Yet Arkady experiences something that Bazarov cannot understand: he loves someone else more than he loves himself. Arkady's brief tryst with nihilism abruptly ends when he falls in love with Katya. In his own words, "everything else has long ago melted into thin air without a trace" (26.126)