Mr. Jaggers decided to give Estella to Mrs. Havisham because he believed she would have the best chance at living a normal life with the old woman.
Mr. Jaggers had been the lawyer for Estella's mother Molly, a poor woman being tried for a violent crime. During the time he was defending her, he had another client, "an eccentric rich lady", who was looking for a child to adopt. In England during the time the story takes place, there were no laws protecting the rights of children, and in his practice, Mr. Jaggers had seen
"children...generated in great numbers for certain destruction...solemnly tried at a criminal bar...being imprisoned, whipped, transported, neglected, cast out, qualified in all ways for the hangman, and growing up to be hanged...pretty nigh all the children he saw in his daily business life, he had reason to look upon as...the fish that were to come to his net - to be prosecuted, defended, forsworn, made orphans, bedeviled somehow".
Mr. Jaggers knew that such a fate was highly likely for the baby Estella, as her father was a criminal and her mother was being tried as such. For some reason, however, he saw Estella as "one pretty child out of the heap who could be saved". He convinced Molly to give her up, telling her, "Give the child into my hands, and I will do my best to bring you off. If you are saved, your child will be saved too; if you are lost, your child is still saved". Molly, having little choice, complied, and Mr. Jaggers took Estella and gave her to Miss Havisham. Happily, Mr. Jaggers was able to exonerate Molly in court, but the "passion and the terror of death had shaken the woman's intellects". She remained emotionally unstable throughout her life, and Estella remained with Mrs. Havisham (Chapter 51).