The Black Order, though proud and ancient, was filled with inadequate people. Human beings that do to their humanity would never be perfect. The members of this order, Exorcist or otherwise, put on a brave front. They acted as though they were as flawless as the little crystals of Innocence they built their lives around, but they weren't.
Koumi Lee, though he tried desperately to make it otherwise, was never good enough for his Lenalee. In his defense it wasn't truly possible for him to ever be everything he had to be for her. He had tried so desperately to be everything for her, a brother, a parent, a supervisor, a friend, and a knight in weird robotic sinning armor. And perhaps if Lenalee had been a normal little girl he would have succeeded. When the Dark Boots had picked Lenalee the Order had taken not only his little sister, but any hope he had of being everything she needed him to be. On his shoulders the Order causally flung the responsibility to take care of all the Exorcists, not just his sister, and to send all the Exorcists to die, including his sister.
Kanda Yu was a failure. First he had failed his most precious person. He would never find them. The intangible chains that held him to the Order would only release him when he released his finial breath. For the duration of his life he would know he had failed in his reason for living. But it wasn't only someone he'd lost in his childhood that he was failing.
Lavi was pathetic excuse for a Bookman's apprentice. His sharp his missed nothing and his mind recorded everything, and, if not for one major flaw, he could have succeeded in his goal. A Bookman, however, can over look no flaw, particular not one like Lavi's. No Bookman needs a heart. No Bookman wants a heart. No Bookman is allowed to possess a heart. And Lavi needed his heart, wanted his heart, and possessed more than just his own heart.
And lastly Allen Walker would never be good enough for anyone. His tainted soul would damn him in the end. He was too much a Noah for the Order and too much an Exorcist for the Earl. He loved too freely without any fear of what the repercussions of that love might be. And so in the same way it started Allen Walker's life ended alone. And the boy that could have saved the world failed to do so simply because he failed to understand the world's need for hatred.