Nothing ever pulls off from an outer perimeter, it’s only inner perimeters of empty loops or holes.

Isn’t that obvious? Try making a circle of a certain size on a flat, empty table, by dragging a string. The circle will become smaller, than the target size because of the drag.

Now drag the string around a gluestick, it can’t be smaller than the gluestick’s circle because the gluestick is in the way.