This work addresses the continuing disagreement between two prevalent schools of thought concerning the mechanism of covalent bonding. According to Hellmann, Ruedenberg, and Kutzelnigg, a lowering of the kinetic energy associated with electron delocalization is the key stabilization mechanism. The opposing view of Slater, Feynman, and Bader has maintained that the source of stabilization is electrostatic potential energy lowering due to electron density redistribution to binding regions between nuclei. Despite the large body of accurate quantum chemical work on a range of molecules, the debate concerning the origin of bonding continues unabated, even for H-2(+), the simplest of covalently bound molecules. We therefore present here a detailed study of H-2(+), including its formation, that uses a sequence of computational methods designed to reveal the relevant contributing mechanisms as well as the spatial density distributions of the kinetic and potential energy contributions. We find that the electrostatic mechanism fails to provide real insight or explanation of bonding, while the kinetic energy mechanism is sound and accurate but complex or even paradoxical to those preferring the apparent simplicity of the electrostatic model. We further argue that the underlying mechanism of bonding is in fact of dynamical character, and analyses that focus on energy do not reveal the origin of covalent bonding in full clarity.