Elizabeth and Colonel Fitzwilliam get along very well. During one visit to Rosings, he asks Elizabeth to play the piano. Darcy leaves his aunt to watch, and Elizabeth playfully accuses him of spreading her poor musical reputation. Colonel Fitzwilliam asks Elizabeth about Darcy's reputation. She relates how Darcy hardly danced at the Meryton ball, even though some ladies wanted partners.
Colonel Fitzwilliam seems at first like another potential love interest for Elizabeth. While Elizabeth lacks the musical accomplishments to recommend her to Lady Catherine, her conversation is sharp and witty, highlighting her independence of spirit.
Darcy tries to excuse his behavior at the ball by saying that he lacks the conversational warmth to introduce himself to strangers. Elizabeth counters with an analogy: if she practiced piano, she might become a tolerable musician. Darcy smiles and says that neither of them performs for strangers.
Here Darcy is trying to apologize to Elizabeth. He suggests that they share underlying similarities. He has gotten past his pride and can now perceive their fundamental compatibility.
Lady Catherine demands to be included in the conversation, and praises her daughter's musical potential—if only she were healthy. Elizabeth notices that Darcy is totally uninterested in Miss De Bourgh.
Lady Catherine sees quality where it isn't there in her daughter. Pride and class prejudice make her blind.