Besides being slightly balmy (i.e., mentally extravagant) Miss Havisham is preparing Estella for her future role in life and wants her to begin early to hone her skills and wants Pip to be victimized by her from an early age. The name is interesting: Havi-sham. The name is said in the way one might offer someone a Danish pastry: "Have a Danish." Havi-sham: Miss Havishem is offering a sham life of falseness and emptiness to Pip and Estella.
The above postings offer some excellent insights into Miss Havisham's possible motivations. I thnk that as a person so traumatised by a failed relationship, she is fascinated with how love can grow and die, and the resilience of the feeling of attachment to another that she herself has never really managed to overcome. It is indeed 'sick fancy' that Pip and Estella are an experiment to her; she scrutinised their relationships and observes each child as if they were laboratory rats. She asks how each of them feels about the other. It is as if she wants to study, analyse and dissect a relationship to try to establish why her own did not work.
There is a definite sense in which Pip is part of Miss Havisham's training program for Estella to make her into the heartbreaker that will be able to take Miss Havisham's vicarious revenge on the male sex. Note the game that they play together. Beggar My Neighbour is an interesting game where the loser is left with nothing and is "beggared." The way that Miss Havisham earnestly implores Estella to "beggar" Pip foreshadows the way that she will beggar other men in her life.
1. When Pip comes to play as the wish of Miss Havisham who has inquired of Uncle Pumblechook if he knows a boy, Miss Havisham tells Pip,
"I am tired,....I sometimes have sick fancies, and I have a sick fancy that I want to see some play."
2.Then, when Estella comes in answer to her call, Miss Havisham tells her to play with the boy. With disdain, Estella exclaims, "With this boy! Why, he is a common laboring boy!" And, Miss Havisham suggests that Estella can break his heart.
3. After Estella ridicules Pip for calling knaves jacks and speaks of his coarse hands and thick boots, Miss Havisham delights in Estella's cruelty to Pip
4. When she asks Pip what he thinks of Estella, Pip tells Miss Havisham that he feels Estella is very proud, pretty, and insulting. Hearing this, Miss Havisham takes pleasure in Estella's being haughty towards him herself.
5. For, she looks at him with aversion as a male: ["She was looking at me then with a look of supreme aversion."]
The first post here is clearly the correct answer. However, since you asked for numerous explanations, here are a couple of possibilities.
One possibility is that Miss Havisham is truly worried about Estella. She might think that Estella needs to have people her own age to socialize with. So it may be that she's thinking of Estella's needs.
A second possibility is that she is tired of dealing with Estella herself. She might want to get Estella out of her hair by giving her someone else to play with.
Those are two options for why she might have done this although, again, the first post's answer is clearly correct.
I think Miss Havisham wants Estella to practice breaking hearts, but a part of that would be teaching her to deny her own in the process. I think just as much as she wanted Pip to fall in love with Estella, she wanted Estella to fall in love with Pip. Dickens talks about Estella's mood swings when it came to her treatment of Pip (chapter 12) and how Miss Havisham seemed to enjoy them; it leads me to believe that Estella was having strong feelings for Pip but being trained that they were to be fought, crushed, and ignored, which must have lead to some pain, inner conflict and confusion for the young girl. Miss Havisham, I think, wanted Estella to learn this feeling of passion young, and wanted her to learn how to reject them young. It would also explain why she always loved Pip, even though she denied it. It was the only love she really ever experienced, but was never allowed to have.