When deriving the work-potential energy theorem, my book states that dV (derivative of the potential energy) is equal to the negative of Fdr without a corresponding explanation. What is the justification behind the negative sign?
As such,there is no explanation,its about definition.
The important thing is,for conservative forces,you can define a potential.Even if you had define dV=Fdr,you would have a consistent theory.The fact that dV=-Fdr,and not Fdr,is not logic,its convention.
In essence,it means that,when positive work is done by the field forces on body,its potential energy decreases,and kinetic energy increases.