The relationship between Pip and Estella in Great Expectations can reasonably be described as complicated. The two meet as children, and as they grow up, adult feelings inevitably enter the picture, making things a good deal messier.
At first, the snobbish Estella doesn't want anything to do with Pip, the "common, labouring boy" as she cruelly calls him. She's set on a trajectory that will see her enter society as a respectable lady. The last thing she wants, then, is to be lumbered with someone much further down the social ladder than herself.
As for young Pip, he's absolutely infatuated by Estella. He may not care much for her caustic insults, but he's positively entranced by her beauty. Even so, he realizes that there's no chance of being with her, given his lowly social origins. This makes him all the more determined to become a gentleman.
Even when Pip becomes a gentleman, however, Estella remains largely cold and unapproachable. She frankly admits to Pip that she has no heart, which is why she marries the rich but brutish Bentley Drummle. In the event, her marriage doesn't work out, and with the revelation of her birth parents' criminal past, her days of being a respectable society lady are over.
As Pip is no longer a young gentleman, he is now pretty much on the same level as Estella. Although this greatly facilitates the establishment of a relationship between the two, by the end of the story, it's by no means clear that it will last.
One of the “great expectations” of the novel’s title is connected to Pip’s conviction that he is intended to become Estella’s husband. He erroneously believes that Miss Havisham expects him to become a well-to-do, polished gentleman who will then be worthy to marry her ward. Pip and Estella meet on his first visit to Satis House. He is hurt and humiliated by her condescending attitude, but his insecurity about being “common” makes him believe that he is unworthy of her. For Pip, falling in love with the cold but beautiful girl is perennially attached to his desire for self-improvement. In fact, Miss Havisham has raised her to attract men but never to care about them. Estella believes that “sentiment” is “nonsense.”
As they grow up, Pip becomes increasingly obsessed with her, and for a long while, it seems unlikely that he will outgrow his infatuation. When Estella is courted by other young men, however, he must accept that she will marry someone else. Taking a keen interest in her happiness, he warns her about a loveless future. Estella declares herself to have no heart and marries the well-positioned but otherwise unsuitable Drummle. In the end, after Pip has traveled and established himself and both Miss Havisham and Drummle are dead, he and Estella recognize the importance of their friendship.
One cannot answer this question without first thinking about Miss Havisham. She was jilted as a young woman and never recovered from the loss; because of her disappointment in love, she has groomed Estella, her adoptive daughter, to break hearts as a kind of revenge on the entire male race. Dickens demonstrates this idea in Chapter 29:
"Hear me, Pip! I adopted her, to be loved. I bred her and educated her, to be loved. I developed her into what she is, that she might be loved. Love her!”
Havisham wants Pip to feel an all-consuming love that is blind and desperate, which he does. As a result of how she was raised, Estella does not have the capacity to love in return. She is cold and calloused, at one point describing herself as heartless:
“You must know,” said Estella, condescending to me as a brilliant and beautiful woman might, “that I have no heart,—if that has anything to do with my memory.”
Miss Havisham has released this beautiful woman into the world to make men feel the pain she felt. Pip falls in love with her, just as Havisham wanted him to, and Estella is aloof and indifferent. She marries someone else, but she doesn't love him either. Dickens wrote two endings, one in which Pip and Estella definitively do not end up together, and a second, less-common ending, in which there is the suggestion that they might get together.
It is worth mentioning that Dickens loves to play with names and has done so here. Estella literally means 'star.' Pip reveres and adores her, and she is bright and beautiful. But she is also distant and cold, and Pip can never actually have her.
Pip falls in love with the imperious Estella. He is the supplicant in the relationship, and she is the queen bee. This is all as Miss Havisham has planned it to be.
When Pip comes into money from a mysterious benefactor, he jumps to the conclusion that it came from Miss Havisham. He believes she wants to make him a gentleman so that he can marry Estella. Of course, nothing could be further from the truth. Miss Havisham raised Estella to break Pip's heart because Miss Havisham's own heart was broken when she was left at the altar.
The beautiful Estella, who has been taught to be cold and does not know how to love, has a haughty and high-handed relationship with Pip. She is the sun, so to speak, and he is the satellite revolving around her.