Twilight releases Cozy Glow from her stone imprisonment, hoping to reform her, after she agrees to certain terms; no hurting anypony anymore or scheming to steal their power, no more conspiring with evil forces, apologizing to everypony she's hurt stuff like that. But the part of the deal Twilight is admittedly the most eager about is for Cozy to tell her about her past, how she got to the point she did, and help Twilight and everypony else understand her.
There's one catch to that last one though… Cozy Glow doesn't actually remember her past. More specifically, she took a potion that erased all her memories of her past, beyond her general objective of syphoning as much magic as she could and obtaining a position of power, shortly before arriving at Twilight's school. But she does have a list of possible origins for herself, that her past self left for her that all contain some motive for what she did. And Twilight's friends are willing to throw out their own theories.
No matter what the real answer, Cozy and Twilight's friends seem to have a good time with it. Much to Twilight's frustration.
Many of these parody other origin stories I've seen for Cozy Glow. Though not all of them. I'll give credit for the ideas other people came up with as best I can.
As the title states, this story was inspired by "The Many Secret Origins of Scootaloo" (great story by the way). But only loosely.