In chapter 2, we are introduced to a transformed Stephen who broods, is purposefully detaches, reads scandalous and heretical poetry, and is obsessed with the idea of Mercedes. Stephen believes that if he wanders the streets enough he'll run into a girl that will transform him. This transformation as a result of meeting a woman would be a kind of "coming of age" for Stephen. And indeed, chapter 2 does end with Stephen encountering a woman, but Joyce frames the encounter in an ironic way that punctures Stephen's character. Actually, many of Stephen's transformation in this chapter feel hollow.
First off, Stephen sleeps with a prostitute which degrades the encounter. Sure, the prostitute might be showing a little interest in Stephen but the encounter itself was transactional in nature. Stephen doesn't mention any of the transaction (which is probably because the narrative is a reflection of Stephen's consciousness) but I think it's safe to assume that he pays the prostitute. The mere fact that the encounter was a transaction cheapens Stephen's actions. Stephen doesn't transform because of his own merit or work but instead pays money in order to have a transformative encounter. As a result, Stephen's "transformation" as a result of his encounter with the prostitute feels a little artificial. The prostitute isn't truly interested in Stephen (aside from his money) and Stephen has no emotional attachment to the prostitute. So although, Stephen narrates the encounter as if it was particularly emotional for him, the scene feels hollow because the reader knows there's no real connection between the prostitute and Stephen.
My second point pertains to the majority of Stephen's actions in chapter two, not just his encounter with the prostitute. A lot of Stephen's changes and actions in this chapter seem to stem from the reading he has done. Stephen feels like he resembles the main character in The Count of Monte Cristo and views Lord Byron as a role model of sorts. Which is all well and good, but sometimes I feel like Stephen tries to hard to be like his romantic heroes. Sometimes, it feels as if Stephen isn't trying to be his own person but Lord Byron 2.0. The poem he writes is in a similar style to that of Lord Byron's. He refers to Emma as E C, just like Lord Byron does. Stephen has sketchy encounters with women just as Lord Bryon does. As a result, Stephen's transformation is undermined and becomes a little more artificial. Stephen isn't transforming into his own person and developing his own views but merely imitating someone else.
I don't want to attack tween Stephen too hard though since most people go through a stage similarly to Stephen (or at least I did). Stephen does grow. He learns to question authority figures like when he talked to the Rector about the prefect's behavior. I think we all go through a stage like Stephen does where we imitate someone we admire. I think imitation is also an important phase too. For instance, the first poem we see Stephen write feels heavily based off an Lord Byron's poetry (Stephen calls Emma EC because that's what Lord Byron does) but this is one of the first poems Stephen writes and its still an important part of his development as an artist. It still gets the ball rolling.
As a result, although Stephen thinks of himself as an old soul who is more mature than the other children his age and his parent's, readers don't necessarily share this sentiment.