Estella tells Pip she has no heart because she lacks sentimentality due to her upbringing by Miss Havisham. However, Estella does have feelings. She just keeps them hidden until later in life, when she is able to start over.
Miss Havisham tells Pip that her heart is broken in chapter 8 (enotes etext p.41). This foreshadows the incident when Estella tells Pip she has no heart. The two events are highly connected. Miss Havisham’s heart was broken by the betrayal of Compeyson and her brother, and it led her to use Estella to get revenge on the male sex. This experience of being taught to tease boys and not love them had a great effect on Estella.
When young Estella does not want to play with Pip, Miss Havisham responds, “You can break his heart” (ch 7, p. 42). It is not the last time Pip will hear this.
And sometimes…Miss Havisham would embrace her with lavish fondness, murmuring something in her ear that sounded like “Break their hearts, my pride and hope, break their hearts and have no mercy!”(ch 12, p. 67)
Estella is taught to think this way, with this sole purpose, from a young age. Pip is nothing more than practice. When Pip falls in love with her, she feels nothing but pity for him.
When Pip confides in Biddy, she asks him if he wants to be a gentleman to win Estella or spite her. Pip realizes that he has made a mistake, and says “the madness of my heart to be so very mad and misplaced” (ch 17, p. 91). Pip does not stop loving Estella, and later asks her why she doesn’t remember their childhood. This is when she tells him she has no heart.
“Oh! I have a heart to be stabbed in or shot in, I have no doubt,” said Estella, “and, of course, if it ceased to beat I should cease to be. But you know what I mean. I have no softness there, no—sympathy—sentiment—nonsense.” (ch 29, p. 162)
It is not true that Estella has no feelings of her own, but she has been taught to bury them so deep that she barely recognizes them. She uses this speech mostly to let Pip down easily, explaining why she cannot love him. At the end of the book she is a slightly broken woman.
There was a long hard time when I kept far from me, the remembrance of what I had thrown away when I was quite ignorant of its worth. But, since my duty has not been incompatible with the admission of that remembrance, I have given it a place in my heart.” (ch 59, p. 325)
Sometimes you have to break something down in order to build it back up again. Estella has to go through the pain of her experiences in order to really, for the first time feel something: friendship.