Why must human beings breathe?

Oxygen is required by the electron transport chain to operate. Many biochemical pathways (for example Kreb’s cycle and ß-fatty oxidation) extract electrons from biomolecules and transfer them to electron carriers NADH and FADH2. These molecules are oxidised back to ultimately generate energy by the respiratory chain, whose last enzyme is cytochrome c oxidase (aka complex IV). The substrate of this enzyme is oxygen, without which the respiratory chain cannot operate and, as a result, energy production is halted. For the record, other enzymes consume oxygen in the human body (for instance cytochrome P450 and NOX), but the bulk is consumed by complex IV.