Why does Miss Havisham invite Pip to Satis House?
Specifically, she claims that she has sick fancies to see the boy play. So, he's coming over for a play date. As readers we come to know over the course of the book that Miss Havisham has a deep hatred for the male race. Part of her life's goal is to get her daughter Estella to also embody this hatred and play it out to all men. This play date with Pip gives Estella practice at making fun of men. She makes fun of him for calling Jacks knaves and for his boots. Miss Havisham is successful in meeting her goal of making Estella a man-hater. This is unfortunate, but the truth.
I assume you are asking about the time that Miss Havisham does this early in the book.
If that is what you are asking, I think there are two answers. The first answer is the reason that Miss...
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Havisham actually gives at the time that she invites Pip. What she says is that she wants someone to keep Estella company -- someone young to play with her.
But it seems likely that Miss Havisham also wants someone for Estella to ensnare. She's raising Estella to break men's hearts and get revenge for her own misfortune, right? So I think she wants to give Estella someone whose heart she can break.