How does Pip discover Miss Havisham's use of Estella in Chapter 38 of Great Expectations?
In Chapter 38 of Great Expectations, Pip is witness to a fight between Estella and Miss Havisham which begins with Estella gradually beginning to "detach herself" from Miss Havisham's arm and ends with Miss Havisham fainting. During this fight, Pip watches as Miss Havisham accuses Estella of being "cold," and Estella responds by saying, "I am what you have made me."
Essentially, Miss Havisham realizes that she raised Estella to be incapable of loving others (the goal was to prevent her from loving men) so that she would not be hurt in the same way Miss Havisham was. However, Miss Havisham never anticipated that Estella would show her learned unkindness to Miss Havisham herself, as this behavior is an ingrained part of Estella's personality.
With regard to your question concerning Pip's discovery of Miss Havisham's "use of Estella," this discovery occurs earlier in the novel. Specifically, Herbert Pocket, a relative of Miss Havisham, tells Pip in Chapter 22 that Estella was adopted by Miss Havisham and "has been brought up by Miss Havisham to wreak revenge on all the male sex."
In Chapter 38, Pip learns about Miss Havisham's use of Estella when he listens to a conversation between them. This is significant because it is the first time that he has seen them act so "opposed" towards each other. Estella is blunt and "indifferent" towards Miss Havisham. In fact, Estella acknowledges that she is Miss Havisham's own creation, saying, "I am what you have made me."
In response, Miss Havisham claims to have treated Estella with "tenderness" and "affection" and to only have desired her love, as any adopted mother would. It is clear to the reader, however, that Miss Havisham has indeed used Estella.
This fight between the two women demonstrates some irony. It is ironic that Miss Havisham desires Estella's love, even though she never taught Estella how to display it. In fact, Miss Havisham has done the very opposite: she has encouraged Estella to act coldly towards others, particularly her male admirers. This does not bode well for Pip, a young man who is in love with Estella, but is about to learn that he is only one of a handful of her suitors.