User blog comment:Kaido King of the Beasts/The Procrastinating Backstory/@comment-4493594-20140724204139

Nice point, Kaido. In fact this plot line got dragged out so much I keep forgetting it exists.

There are a couple of things I can imagine regarding Corazon and his demise. Generally, we can assume that he did something that made Doflamingo stop thinking of him as his "family". Maybe:
 * He disagreed with Doflamingo on a certain course of action and threatened to get in Doflamingo's way.
 * He was more popular among the Donquixote Pirates than Doflamingo and was a threat to his position as captain.
 * He got fed up with being a pirate altogether.
 * All of the above.