Males die of suicide more often because they use more successful methods. It makes sense that a female doctor would be much more successful than the average female due to her education.

Most women use pills, men use guns.

Even when you control for method, men are more successful at suicide than women.

The ratio is just as lopsided with countries with strict gun control (e.g. Britain).

Alternative hypothesis: death is the goal for many men, while women often use suicide attempts as a cry for help.

Agreed. Randomly and anecdotally, I am reminded of Iris Chang, who was a famous author responsible for our knowledge of the Rape of Nanking.

Her cause of death was brutal, and she was going through immense pressure during her last research project. A self-influcted gunshot to the mouth sounds like a horrible way to go.