Amir decided to go to Kabul to save Hassan's son and to repay by saving Sohrab that is Hassan's son, thus by doing this he can somehow lower his guilt of not saving Hassan.
He went back to prove that he still loves his hometown and lower his guilt for not saving Hassan. In the end Amir puts Sohrab in an orphanage and files for an adoption petition. He also cries in remorse and asks him for forgiveness. But the truth is that Sohrab cried his heart out in the end but never forgave Amir for the huge mistake he made.
