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If energy is stored in chemical bonds, and bond formation is always an exothermic process, doesn't that imply that bond formation both stores and releases energy? How is this possible? I'm clearly not understanding some basic tenet of chemistry. For example, H+ and OH- neutralize to form H2O.
As you said, it's true that breaking bonds always absorbs energy. But breaking bonds is just halfway through for a chemical reaction. Forming new ones releases energy. The difference within determines a chemical reaction endothermic or exothermic. For ATP hydrolysis, the bonds within an ATP and a water molecule break, which absorbs energy, as you might think. Then the new bonds formation to form an ADP and a phosphate releases a lot of energy.