Disclaimer: I do not and I never will own Naruto no matter how much I wish for it.
Kakashi never cried. Not when Sakumo committed suicide, not when Obito died.
The memorial now holds another name, Kamikaze Minato, the fourth hokage. He, who sacrificed himself to save the village, his soul in exchange for many other lifes. He was hesitant, he had a child to look after, but he still had to do it. It was his duty. The night they held a funeral for the Yondaime, everyone wore black. Everyone cried for the yellow flash that valiantly saved the village. He was a hero. But Kakashi did not cry. He did not break rules and one of the rules in the shinobi book was: Shinobi must never show any form of emotion or cry. So Kakashi did not cry.
When Rin transferred the last of her chakra in a desperate attempt to save Kakashi's life, Kakashi did not feel anything. He made a promise to Obito, the one whereby he was to protect Rin with all his life, so why was his body not resisting? Why was he allowing Rin to waste her remaining chakra to him? He knew that he did not deserve it. It felt wrong to take it. His life was not his. It belonged to others, others who gave up everything just to see the silver haired shinobi live. He was a genius, one who was probably more useful as a tool to the village. Maybe that explains why they were willing to make the exchange.
So when Obito cried, Kakashi was glad.
Hatake Kakashi was always on time. He was never late. He did not oversleep, did not dilly-dally and did not keep rereading the icha-icha series seven times. No, he did not do any of that, instead there was something else he did everyday. He stood at the stone.
The jounin could not afford to be late unlike some Uchiha he knew. So he limited himself to standing at the memorial for ten minutes a day. Each day, reporting about how he failed another group of genins. But Obito was still as annoying, insisting that he stood at the stone awhile longer. He enjoyed seeing Kakashi telling tales about his day, especially about a particular group of three which managed to pass.
Old habits never die, Kakashi was always on time, Obito was always late and Kakashi was glad.
He tells himself it is never his fault (thatteamyondaimenolongerexist) and that he was and will be a ninja who never defied the rules. He was not angry with the white fang's death because he knew his father was to blame. His father was not the reason why Kakashi stuck to the rules because the very basic of the shinobi rule was never to show emotion.
The ninja in the book is the one who possesses the discipline to follow all the rules. Kakashi always thought he was a ninja. Yet only until the moment Kakashi no longer uses this as an excuse will he ever become one.
He blames everyone, but never himself.