The major reason for this is the fact that the fear caused by the Haitian Revolution made whites in the Caribbean feel that they needed to do something to make other rebellions less likely.
The plantation owners on other Caribbean islands saw the Haitian rebellion and realized that it could happen to them. Of course, they did not want to be killed by rebellious slaves and so they tried to think about how to avoid this fate. Since harsh treatment of slaves had not worked, they started to think about going the other direction.
In addition, the rebellion made some in Europe rethink the idea of slavery. They started to think about slavery in the context of the French Revolution and its ideals. In other words, the fact that slavery was bad enough to cause this sort of a rebellion gave them reason to consider whether it ought to be abolished.