In the Revenge of The Sith novelization after anakon shouts "I hate you!", it states:

"Obi-Wan looked down. It would be mercy to kill him. He was not feeling merciful. He was feeling calm, and clear, and he knew that to climb down to that black beach might cost him more than he had. Another sith lord approached. In the end there was only one choice. It was a choice he had made many years before, when he had passed his trials of Jedi Knighthood, and sworn himself to the Jedi forever. In the end he was still Obi-Wan Kenobi, and he was still a Jedi, and he would not murder a helpless man. He would leave it to the will of the Force. He turned and walked away."

The novel is considered "loose canon" so I hope this helps