Let's begin by stating the obvious: Stephen does not seem to be a very good teacher. He is aloof and is busy thinking about Aristotelian metaphysics while his class is going on. He believes that he is "above" his students, and first demonstrates this by making a joke about Kingstown pier being "a disappointed bridge" that the students do not get. In this case, Stephen is playing on Ireland's sense of isolation from Europe and its disconnectedness, something a bunch of adolescents could not be expected to understand.
Similarly, Stephen's riddle that is not actually a riddle is kind of like an inside joke with himself. The only time he seems to make a connection is when the boy Sargent begins to make him think of his mother's love and there is a real moment of empathy between them. Stephen comes across as not such a nice guy in this chapter, but the more sympathetic view is that he is trapped in his own head. Throughout the book, we will see just how alone Stephen is, and how, brilliant as he is. Smarts, however, can only take him so far.
The big "theme" of this chapter is history. Stephen begins by discussing the general Pyrrhus who led a campaign against the Romans, but was exhausted by his own victories. Here, we get a sense of Stephen's dislike of violence (a dislike Pyrrhus shares), and the smaller Tarentum rebelling against the much more powerful Romans brings to mind the relationship between Ireland and England at the current time. Later, Stephen begins musing on Aristotelian metaphysics, and how there is a moment where an event actually takes place and all of the different possibilities for what could have happened get scattered to the winds. The simple way of viewing this internal dialogue is that Stephen is musing on how things might have been. The unfortunate history of Ireland plus his experience with his late mother send him into a hyper-abstract self-debate about how and when an event gets lodged in time and is beyond reversal.
Mr. Deasy has a decidedly different view of history than Stephen does. He is an English sympathizer, though he claims to have a long Irish history and to understand the country's problems quite well. He has no problem scape-goating people left and right (first the Jews and then women), but views history as something ordained by God that is moving toward a fixed purpose. (It's interesting to contrast Deasy's history as blame with Haines's comment that history is to blame.) For Deasy there is no doubt about how history has unfolded; he does not struggle with it as Stephen does. Deasy's private memories of Irish life and his ancestry are woven perfectly into his more public view of history. Stephen, by contrast, cannot reconcile his personal experience with the public telling of history. History is something that happened to Stephen rather than something in which he is involved. As a result, he thinks of history as "a nightmare from which I am trying to awake" (2.157).
Mr. Deasy comes across as not smart in the chapter, and it is from his tongue that we get the first whiff of anti-Semitism in the novel. Deasy's prejudice against the Jews is strong, and yet it is hardly an exaggeration considering how common anti-Semitism was in Ireland and throughout Europe at the time. In 1904, Jews were being forced out of Eastern Europe and were settling in the West, where they were often ostracized and mistreated. Unfortunately, anti-Semitism was incredibly widespread. We will see in two chapters how Joyce turns this prejudice right on its head by making his protagonist a Jewish Irishman named Leopold Bloom. (To many Irish at the time, the mere idea of a Jewish Irishman would have been an oxymoron). It's a delightfully mischievous move on the part of the author, but it also is an example of his forward thinking and empathy during a time when anti-Semitic writing was extremely common.
In the "Nestor" section of the Odyssey, Telemachus goes to see the master charioteer Nestor in an attempt to get news of his father. Nestor knows that Odysseus's homecoming will be hard, but affirms that Telemachus is becoming a man and relates some of the history of the Greeks. He includes Agamemnon's homecoming and death to foreshadow how difficult it may be for Telemachus and Odysseus. Mr. Deasy is set up in the chapter as a "Nestor" figure. He affirms Stephen's growth by predicting that he will not remain long at the school. Yet, unlike Nestor, he does not demonstrate his wisdom in showing how hard Stephen's task will be. Instead, it is through his ignorance and his insular thinking that he shows Stephen how hard it will be to surmount myopia and prejudice.