The current situation with Instagram is that users can only remove followers if their account is private. The new feature being tested will allow account holders to remove followers without the followers being informed.
This initiative follows other moves to give users more control over their accounts. This includes giving account holders the ability to mute people they follow and an experimental do not disturb feature.
"Instagram… now a mature social network with over a billion users… wants to eliminate the content that might drive [users] away, whether it's harassment or too-frequent notifications." Source: Endgadget.
Original soruce: The Verge.