Warning! Spoilers Ahead For Shadow and Bone season 1 and the Six of Crows novels.
Shadow and Bone season 1 show’s Kaz Brekker’s bitter hatred of rival crime boss Pekka Rollins, but it doesn’t explain why Kaz hates him so much. The details of that backstory are revealed in Leigh Bardugo’s novels Six of Crows and Crooked Kingdom, which focus primarily on Kaz and the rest of his Ketterdam gang, the Dregs. Future seasons of Shadow and Bone will likely reveal more about Kaz’s past, but the story of his vendetta against Pekka is already known to those who’ve read the books.
In the Grishaverse books, Kaz Brekker – originally named Kaz Rietveld – was born in the Kerch village of Lij. After his father died, Kaz and his older brother Jordie came to Ketterdam with a bit of money in their pockets to start a new life. Kaz was only nine years old at the time. Unfortunately, the boys were scammed out of the money they brought by none other than Pekka Rollins, then going by the name Jakob Hertzoon. After being swindled by Pekka, the brothers were forced to live on the streets, where they struggled to survive.
The con alone would have been enough to earn Kaz’s ire, but his hatred of Pekka runs even deeper for a more tragic reason. Because of their poverty, the Rietveld brothers were incredibly vulnerable when Ketterdam was hit by the Queen’s Lady Plague. Both boys caught the illness, and while Kaz managed to survive it, Jordie wasn’t so lucky. Both brothers were assumed dead after passing out from the fever and were subsequently loaded on a barge packed with the corpses of plague victims. Young Kaz escaped and swam to shore using Jordie’s dead body as a floatation device – an experience that traumatized him for the rest of his life.
Understandably, Kaz held one man particularly responsible for his brother’s death – Pekka Rollins. Because of Pekka’s con, he and Jordie were robbed of the ability to protect themselves, indirectly leading to the older boy’s death. Kaz’s work with the Dregs gang (also called the Crows) and rapid ascension through Ketterdam’s underworld was all in the interest of attaining enough power that he might one day be able claim his revenge, his visceral hatred for Rollins, and desire to never be weak or naive again underpinning everything Kaz does.
Of course, Pekka Rollins himself has no recollection of his connection with Kaz; to him, Kaz and Jordie were just two more gullible, sad marks in a long list of people Pekka has cheated. In Shadow and Bone season 1, during a scene where Pekka confronts Kaz for stepping on his turf, Kaz asks if the two of them have ever made a deal before. Pekka says they haven’t, showing that he doesn’t realize the aspiring crime lord in front of him is the same boy he conned years ago. It's an insult to be so little remembered when Pekka ruined Kaz's life, but it's also to Kaz's advantage that Pekka doesn't know who he is – and Kaz Brekker always uses every advantage he can get. If Shadow and Bone stays true to the books, that could lead to some interesting developments for Kaz down the line.