Why did Sir Arthur Conan Doyle decide to kill off this character?

Question

In the short story "The Final Problem", Sir Arthur Conan Doyle made the decision to kill off Sherlock Holmes (although he did bring him back again in the story of "The Empty House"). This was met with great disapproval from the fans, who didn't want to see their favorite detective dead. Why did he decide to kill off his most famous character?

Answer 1

He simply got tired of writing about Holmes, and he wanted to focus on his other writing.

I'm going to quote from a book called The Best of Sherlock Holmes, by Wordsworth Classics:

However, even before the ink was dry on the manuscript of 'The Copper Beeches' its author had wearied of Sherlock Holmes. In fact, by the end of 1891 he had written to his mother,one of Sherlock's greatest admirers, stating that he was thinking of 'slaying Holmes in the last [story]. He takes my mind from better things.' His mother prevailed upon him to change his mind, which for a time he did. The 'better things' to which Conan Doyle referred were his historical novels, which he considered to be 'serious literature' compared with his catchpenny detective stories. Also, on a practical level, churning out twelve ingenious plots in a year was hard, demanding labor.

So we see that he was getting burnt out, and he wanted to do other things.

Conan Doyle's disenchantment was growing when he was approached by the editor of The Strand for a further twelve stories. In order to put him off he asked for what he considered to be a ridiculously high fee of fifty pounds a story, fully expecting to be turned down...

...

After he killed him off, the fans weren't so happy. One lady even sent him a letter calling him a brute.

Conan Doyle's reaction [to the criticism in response to him killing Holmes] was somewhat different. Maybe with that letter of abuse from that irate lady in mind, he expressed grim satisfaction: 'Thank God, I've killed the brute.'

So he felt that it was too much work and he was too tired of writing Holmes stories, so he killed him off.

So why did he bring him back in The Empty House?

Well, before he decided that Holmes wasn't dead, he heard a story in 1901 that made him think about a family who was being haunted by a dog...

For years he disregarded all pleas to resurrect Holmes, but in 1901 when he heard a friend's account of some legends of Dartmoor he conceived a mystery story about a family supposedly haunted by a spectral hound. He was very pleased with the idea of this story, which in a letter to his mother he described as 'a real creeper' - a phrase he was later to repeat when selling the story to Greenhough Smith of The Strand. In developing the plot, Conan Doyle realised that he would require a detective hero to be involved with the strange events and eventually to solve and explain the mystery. He was sensible enough to see that there was little point in creating a new character for this task when he already had one he'd made earlier: Sherlock Holmes. So, one suspects, with some reluctance, Conan Doyle converted his ghostly-dog saga into a Sherlock Holmes adventure and called it The Hound of the Baskervilles. However he was adamant that this story did not herald a permanent return - Sherlock Holmes was still dead - and that this investigation took place prior to Reichenbach.

So he brought back Holmes for a short while, but it was set before he died. The fans reacted...

Now that Sherlock Holmes had appeared in print once more, readers and publishers alike hoped that the author could be persuaded to relent and drag the fellow up from his watery grave for more adventures.

...

By 1903, Conan Doyle was a much more relaxed and confident man and the idea of writing further detective stories was no longer abhorrent to him, so when the New York publisher of Collier's Magazine offered him four thousand dollars per story he at last gave in.

TL;DR:

He stopped because he was worn out of writing Holmes stories, and he started again because he was no longer as burnt out.