Sherlock Holmes was contemplating suicide when he first laid eyes on John Watson. Sherlock was bent over his microscope, the famous brain moving faster than a bullet train with a thousand different thoughts vying for his attention. Suicide was a solution to a problem he was in the midst of and, as every scientist does, he was evaluating his solution for errors.
Would anyone actually miss him if he were to die? The normal list of people who would normally care, Sherlock understood, were friends and family. He had no friends. Check one. Mycroft wouldn't mind as long as it didn't become a scandal or bother Mummy and Dad. They actually might care, boring average people that they were. But they were old, they didn't have long to suffer. Mycroft would take care of them.
So people as individuals would not care if Sherlock was gone. But would the world as a whole be less off without the detective? Anderson the Idiot didn't think so. But Sherlock's contributions needed to be examined. He had already completed his catalog of cigarette ash as well as a few other papers pertaining to the art of deduction. The work Sherlock did for Scotland Yard would absolutely be considered positive. He had assisted with (solved) several cases involving serial killers, kidnappers and various other criminal undertakings. He saved lives. DI Lestrade certainly appreciated Sherlock's help. But would his team be unable to function without Sherlock's assistance? Considering the Yard had been around for hundreds of years Sherlock assumed the life of one sociopath would not be a significant loss to London's finest. So society would not miss his contribution.
The final matter to consider was the detriment Sherlock's existence brought to the world. He knew he was an unsavory individual in personal relationships, not quite understanding human interactions. He often pickpocketed people (even police officers), he drove without a license (taking a test would be tedious, Sherlock knewhow to drive), and he frequently funded the low lifes of London with his drug habits. And here was where the morals of life and death came into play. Could his ill behaviour be excused by the good he had tried to accomplish? How exactly did the scales fall? Could Sherlock leave this world with his life unbalanced, leaning towards a negative outlook? Did it even matter? Did he even care? When it all came down to it Sherlock was bored.And he was tired of pretending. Pretending to be normal, and happy and content with his life. He just wanted out.
So Sherlock came to the conclusion while bent over his microscope that tonight he would go find his old dealer and dose up one last time. No one could stop him. It would be easy. He had a flat to himself after all.
Then John Watson walked into the lab.
And Sherlock saw everything. He saw the medical degree in his hands. He saw the military history in his tan lines, posture, and limp. He saw the three weeks without a proper sleep in the bags under his eyes. Even the PTSD was obvious. But so were the multiple suicide attempts. John Watson, who had served in Afghanistan or Iraq, had a revolver in his desk drawer. He took it out frequently, staring at the smooth metal reflecting the lamp light. He took it out whenever he had a nightmare. In fact, he had examined the weapon for a great length of time that very morning. The therapist didn't know. No one knew. Except Sherlock Holmes. And as Sherlock deduced everything about John Watson he saw something else. He saw himself in John. They were both floating, drifting in a world where they didn't fit. John was a soldier without a war. Sherlock was a genius surrounded by idiots and yearning to stop being lonely. They were both in a hopeless tailspin.
What Sherlock saw in John Watson was the last chance anyone was going to get to save his life. So Sherlock took the leap, almost without considering the consequences, and offered the flat share to John. He told himself it was because he planned to snub his brother. See Mycroft, facilities are unneeded for recovery. I fixed him without your precious institute.
But really he just wants to save John because maybe, if John can be saved, so can he. Maybe they can fix each other.