In order to get a master doctor, the doctor will have to perform a large amount of cures and/or herb studies. Herb studies are difficult two reasons: 1. Villagers don't normally study herbs on their own (although every so often they will, but it's only once and then they go back to other activities).
2. Sometimes when you drag a villager onto an herb, he/she will go into "Herb Studying" mode and go from herb to herb studying them, however, they have a tendency to get caught on objects in the game and forget what they were doing.
Basically, herb studying in an impractical way to reach Master Doctor for these two reasons. Performing cures is a much easier way, as doctors will do this automatically if someone is sick. There are several ways to create more sick people:
1. Grow your population
the more people you have, the more sick people your doctor will be able to heal.
2. Let the fire go out
The fire reduces the likelihood of sickness, so if you are trying to train a doctor, let it go out so there will be more cures for your doctor to perform.
3. Prepare a "Sick" stew
There are certain stews that make villagers sick. By feeding this stew to many villagers, your doctor will be able to perform a large number of cures all at once.
If you're lucky, you may also get an event that will create a master doctor. I also hear that end-game there is another way you can get master doctor as well
