Question

Why were Roman consuls awarded the power of the veto?

Answer 1

There were always two consuls in power at a given point of time. The right to veto the other's decision was seen as a measure to prevent the abuse of power by the other consul.

Answer 2

The power of veto was not just restricted to the consuls. All officers of state (consuls, praetors, censors, aediles and quaestors) had the power of veto. Officers of the same rank could veto each other and officers of higher rank could veto officers of lower rank.