On 20 July 1402 Bayezid I was defeated by Timur (Tamerlane) at the Battle of Ankara. This sparked a succession crisis lasting 11 years in which Mehmed I had to fight challenges from every single one of his brothers, some of whom were backed by foreign powers -- the Timurids and Byzantines.

It nearly destroyed the Ottoman state, so Mehmed I's grandson Mehmed II decided to formalize fratricide as a succession mechanism. It was intended as a Darwinian feature for the Ottoman state. Traditionally, Ottoman princes would be sent out around the Ottoman lands to hold various administrative posts, particularly governorships, to teach them statecraft and to try to ensure loyalty to the throne in far-flung or willful provinces.

The reasoning behind the acceptance of fratricide was that if a prince couldn't secure the kind of support from local nobility, cavalrymen, and Janissary commanders needed to kill his brothers, as well as merchants and clergy to help legitimize him, he would neither be able to bind the realm together, nor protect it from foreign powers. It was also rightly reasoned that fratricide wouldn't be overcome merely by filial affection, and therefore it would be easier to embrace it. Additionally, fratricide being the known order of the day encouraged early, decisive action to consolidate power quickly, so as not to draw out proceedings like Mehmed I's brothers did, and therefore ensure a certain level of stability.

Eventually actual fratricide came to be viewed in a negative light. Mehmed III ended up killing 19 of his brothers, and in response his successor Ahmed I abandoned the practice in 1603, instead opting to imprison his brothers in the Kafes ("cage") of the Topkapı Palace.

Source- Finkel, Caroline. Osman's Dream: The Story of the Ottoman Empire, 1300-1923. New York: Basic, 2006