Student or Learner
If I would say "I could have been president"...why is there not a "a" in front of president, as " I could have been a president"?
President is a title of the top most post of an organization, company, trade unions, universities, and countries. If you have assumed to be the president of a specific country say America, as clarified by Soup you can not use any article before president. However, if you use a modifier, or you have desire to be president of any establishment, you can say;
I could have been a better President.
I wish, I could have been a President of a reputed company.