A large amount of the oil and natural gas used in the U.S. is directly a product of offshore drilling and many jobs exist because of it. For example with the ban against offshore drilling eliminated in Virginia the economy is stimulated there by the creation of more jobs. This is an example of the offshore drilling option providing fuel both literally and economically as the unemployed find work.
Offshore drilling also greatly increases the American fuel supply. Numbers of fuel gallons can be in the millions based on how many barrels of oil are pumped, plus there's the added benefit of thousands of cubic feet of natural gas that further makes the case for offshore drilling.
Land platforms and drills have to be removed when they are no longer needed and there is cost involved with that process. By utilizing offshore drilling even when the rigs are no longer in use, the platforms do not have to be dissembled and removed but can stay in place and act as reefs, if unnatural ones, and can shelter many different fish species.
One of the largest benefits of offshore drilling is to keep one step ahead of international competitors in terms of oil and natural gas supply and cost. For example some of the continental shelf could be explored by other nations for its supply if the U.S. does not take advantage. Additionally, by pumping more of its own fuel the United States is less on reliant on outside sources and is able to spend less on competitors' fossil fuels. Many politicians are in agreement that it would be better to rely on domestic fuel rather than foreign.