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I understand the problem, but I am unsure of why they use the work done by the spring instead of the work the glider does on the spring in the work-energy theorem, and the book also makes it sound like you cannot use the work the glider does on the spring in the work-energy theorem and I am clueless as to why it is so?

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The work-energy theorem refers to a system.

The system in your example is the glider.
So it is the work done on the glider by an external force (provided by the spring) and the change in energy of the glider which are the relevant quantities.

You could choose the spring as the system and then the glider will provide the external force on the spring and it will do work on the spring this will result in a decrease in the elastic potential energy stored by the spring.
Note that in this case as the direction of the force exerted on the spring by the glider and the direction of motion of the glider are opposite the work done by the glider on the spring will be negative.

You could choose the system as the spring and the glider (and the Earth) with no external forces acting.
Then no work is done on the system by an external force and the elastic potential energy lost by the spring is equal to the kinetic energy gained by the glider.

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Because the object you are now analyzing is glider, so you have to consider any work the object obtained or lost.

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