Saving Face
The close friends list feature on Instagram is to make posts on your profile story only visible to a specifically curated list of people. This way you can keep other friends, family members, or strangers from seeing some of your more personal activities online. It looks a little desperate for someone to demand to be placed on a close friends list.
After demanding to be put back on, this person receives the clear message that they were intentionally removed from the list. When they make a distasteful remark in the heat of the moment, they try to cover it up as an accident.