Lady Vengeance

A Christian musical procession waits with a symbolic block of tofu outside a prison for the release of Lee Geum-ja (Lee Young-ae), a recently reformed female prisoner. Convicted of kidnapping and murdering a 5-year-old schoolboy, Won-mo, 13 years earlier, the case and Geum-ja became a national sensation because of her young age, angelic appearance, and eager confession to the crime. However, Geum-ja became an inspirational model for prisoner reform during her incarceration, and her apparent spiritual transformation in prison plus her beatific conduct toward other inmates, who gave her the nickname "Kind-Hearted Geum-Ja," earned Geum-ja an early release on her sentence. As Lee Geum-ja emerges from prison, she flips the tofu to the ground and sidesteps the procession, intent on revenge.
Donning blood-red eye shadow and cutting off her little finger, Geum-ja quickly shows that her "kind-hearted" and inspirational behavior in prison was a cover to earn favor and further her intricate revenge plans. She had, in fact been the prison Witch, a title given to the most powerful female prisoner, and her angelic demeanor and assistance earned her many followers and loyal allies. Once paroled, Geum-Ja immediately visits the other paroled inmates, calling in favors that include food, shelter, and weapons. She also begins work in a pastry shop run by a chef who'd previously volunteered at the prison, and starts an affair with the shop assistant, a young man who would be the same age as her victim, Won-mo, had he not died.
After the detective from her case stops in the bakery by chance, it is revealed that Geum-ja did not smother Won-mo. The detective himself was aware of her innocence, but helped her fake certain crime-scene details, such as the color of a missing marble, to ensure her confession looked credible. As a young high school student, Geum-ja had become pregnant and, afraid to go home to her parents, turned to Mr. Baek (Choi Min-sik), a teacher from her school who had said she was sexy, for help and a place to live. Mr. Baek was not altruistic in his aid and expected Geum-ja to provide sex and assist in his kidnapping/extortion racket. Mr. Baek used Geum-ja to lure 5-year-old Won-mo away and deliver the child to him, with the intent of ransoming the child, but Mr. Baek unintentionally killed the boy while Geum-ja was out. Mr. Baek then kidnapped Geum-ja's infant daughter and threatened to murder the baby if Geum-ja did not take the blame. Geum-ja spent 13 years in prison planning revenge on Mr. Baek for the murder of Won-mo, causing Geum-ja's child to grow up without a mother, and for sending Geum-ja to prison in his place.
Geum-ja searches for her daughter and discovers that she was adopted by Australian parents. Jenny, now an adolescent, does not speak Korean and does not initially embrace her mother, though she returns with Geum-ja to Seoul for a visit and to bond.
Geum-ja plans to kidnap and murder Mr. Baek, who is now a children's teacher at a children's preschool, with the aid of his wife, another ex-convict Geum-ja planted with him. Mr. Baek, who knows Geum-ja has been released and is aware of her plans, attacks his wife and hires thugs to ambush Geum-ja and Jenny. In the ensuing battle, Geum-ja kills both thugs, while Mr. Baek is subdued by his wife.
Mr. Baek wakes up gagged and tied to a chair in an abandoned school house in the middle of nowhere. Geum-ja, eager yet hesitant to kill him, threatens Mr. Baek until his phone alarm distracts her. Pulling it from his pocket, she discovers the red marble missing from Won-mo's crime scene hanging on his cell phone strap. It had been taken as a trophy. She is horrified to see several other children's trinket trophies also hanging from the strap. Geum-ja beats Mr. Baek and then rips his apartment apart to discover snuff tapes of the other children that Mr. Baek murdered. He had not been part of a ransoming racket, but would kidnap, torture, and murder a child from each school he worked at because he finds small children annoying. After killing each child, he would fake a ransom call to the parents, collect the money, and move on to a different school. He was saving up the ransom money to buy himself a yacht.
Sickened by the realization that four more children died because Geum-ja did not turn in the real killer 13 years ago, Geum-ja and the original case detective contact and transport the parents and surviving relatives of the missing children to the abandoned school. After watching each tape, and being told Mr. Baek is in the next room, the group deliberates on Mr. Baek's fate, ultimately deciding to murder him collectively, with the audio of their discussion amplified for him to hear. Prepared with raincoats and wielding a variety of weapons, they take turns on Mr. Baek until the last person, an emotionless grandmother, kills Baek with the school scissors of her murdered grand daughter. They take a group photo, ensuring that none of them can turn in the others without implicating themselves, and bury the corpse outside.
Geum-ja, the detective, and the relatives all converge on Geum-ja's bakery, where they eat a cake and sing a collective birthday song for their deceased children, feeling lighter and noticing it is snowing outside. Afterwards, while removing her red eye shadow, Geum-ja sees the ghost of the murdered child and a chance to ask him for her long-awaited redemption. Before she can do so, he transforms into his grown self (the age that he would have been if he had lived) and gags her before she can repent. When Geum-ja later approaches her apartment with a cake box, she notices Jenny. They embrace before Geum-ja opens the box to reveal a white cake that resembles a block of tofu. She instructs her daughter to "live white", as pure as tofu. Jenny tastes the cake and says Geum-ja should live even more purely. As they stare up into the snowy sky, Geum-ja weeps and sobs uncontrollably, her face buried in the white cake, while Jenny hugs her.

Question: Why did Geum-ja want revenge?