If you didn’t already know that Mulligan was a medical student, here he proves it. He doesn’t understand why Stephen is so offended by his “beastly dead” comment. I suspect most readers are also a little confused by this–or at least about why Stephen has been holding on to it for so long.
You get (at the bottom of the page) a classic Stephenism–that he is not upset about the insult to his mother, but rather “of the offence to me.”
What does Stephen mean by this, and why is it coming out now? On the simplest level, Stephen is perhaps as offended by Mulligan referring to him as “only Dedalus” as he is about his mother being “beastly dead.” Further, if Mulligan respected Stephen, or saw him as a social equal, or saw him as the promising artist Stephen sees himself to be… he wouldn’t have said that. It’s another small detail that shows you how Mulligan’s interest in Stephen is insincere. The anecdote also serves to deflate, or put into context, Mulligan’s invitation to go to Greece. I think Stephen also is offended because his mother’s death is such a huge presence in his present life–he might like to escape his fixation on it, but as we’ve already seen, the experience still haunts him.
So who was Sir Peter Teazle? First, a character in Richard Brinsley Sheridan’s School for Scandal, a hugely popular play from the late 1700s. Second, a prize racehorse! I had no idea about that second one, but it’s a nice Ulyssean fit.