The Following/Follower relationship
Many Celebrities need a way to publish their news and information without having to add every fan as a friend. Instagram helped those celebrities achieve that goal easily with its following/follower system.
Facebook allows a person into their private lives
Many celebrities want to keep their private lives away from their fans and only post to them what they want. Facebook is considered more intrusive compared to Instagram and this is why celebrities prefer Instagram over it.
Instagram appeals to narcissists
Some celebrities are narcissists. Instagram appeals to narcissists as it gives them the exaggerated self importance they are looking for.
There is no limit to the no of followers
Facebook has a limit on the no of friends one can has while Instagram doesn’t have any limit for followers. Facebook implemented a following system but it failed to take over Instagram.
To easily allow their fans to reach them
On Facebook a person needs to send a friend request before he can be connected with someone but on Instagram a person just needs to follow the one he is interested in.
It’s a broadcasting platform
Instagram was designed to be a broadcasting platform and those platforms usually appeal to celebrities as they easily allow them to update their fans. (See Why do Celebrities like Twitter?)
To market for themselves
Many celebrities use Instagram as a marketing tool to gain more fans , to make their brands powerful and to create news that can make them more popular.
To show off their pictures
Many celebrities use Instagram to show off their pictures or their extravagant lives. The way Instagram was made easily allows this to happen.
To interact directly with their fans
Some Celebrities use Instagram to interact with their fans directly without having any strings attached unlike Facebook where accepting a friend request usually leads to long term commitment. (See Why celebrities earn so much money?)
The term ‘Friend’ doesn’t work for celebrities
On Facebook the term ‘Friend’ doesn’t really appeal to celebrities as many celebrities don’t want to be friends with people they barely know.