Based on the level of Gender Discrimination in times past, there are more male Doctors and more female nurses.
Over time, the margin has reduced but there's still a quantifiable difference in the number. There wouldn't be efficiency in the medical system if attending to patients in Gender-based due to this numbers.
The only possible option is 'choice' and this would be dependent on the availability of Doctors. This choice also has to be sorted by a system to avoid any form of Discrimination.
Hence, you get the Doctor you prefer if that Gender is available.
In Nigeria, where such a system might not be workable for now, the choice thing cannot even work.