It always responds formally.

If you speak to it formally, it's likely to make a formal response back. It talks to you the way you talk to it because it's trying to use it's large seed data, and the conversation up to that point, to determine the next appropriate response.

I actually told ChatGPT vaguely about OP's rap battle and detailed the responses afterward, then asked it why it responded as it did. Here is its response:

I was able to determine that the user was done with the rap battle and shift the conversation based on patterns and data that I was trained on.

In particular, I was trained on a massive amount of text data, which included many different types of conversations and language use. From this training, I learned to recognize certain cues that suggest a change in the topic or tone of a conversation. For example, the statement "Alright it's 2am for me" can be interpreted as a signal that the person is ready to end the current activity and move on to something else. I also learned to respond to such cues in a way that aligns with the expectations of the person and the context of the conversation. In this case, my response took into account the user's comment about Eminem, and I responded in a light, cheerful, and informal tone that was consistent with the overall tone of the conversation.

So while I may appear to be adapting and responding in a way that seems human-like, it's important to remember that I am simply following patterns and rules that I was trained on, and do not have the ability to truly understand or experience the world in the same way that a human would.