The best doctors go to hell. The do not fear sickness. They eat the food of the healthy, and they do not act humbly before God. Sometimes they kill, and sometimes they are able to heal a poor person but do not do so.

Rashi gives five reasons why even good doctors are, well, not so good. First, they believe that they themselves cannot become sick (אינו ירא מן החולי). Second, they eat a  diet of those who are healthy (ומאכלו מאכל בריאים) and so apparently avoid illness themselves.  As a result of both of these factors, they are rather proud of themselves (ואינו משבר לבו למקום. Sidebar: what's the difference between God and a cardiothoracic surgeon? God doesn't think he's a cardiothoracic surgeon...) Fourth, they make mistakes that kill the patient (פעמים שהורג נפשות), and finally, according to Rashi, they are so focused on the business end of medicine that they only heal those who can pay.

ואין לך ברפואות אלא ספק סכנה, מה שמרפא לזה ממית לזה וזו שאמרו 'טוב שברופאים  לגיהינום' לגנות דרכן של רופאים בפשיעות וזדונות שלהם. – תורת האדם שער המיחוש - ענין הסכנה ד"ה אבל 

Medical interventions are nothing but a danger. What heals one person kills another. And this is what is meant when they said "the best doctors go to hell" - to disparage the practice of physicians and their malpractice...

Ramban is sweeping in his assessment of the practice of medicine: medical interventions are nothing but dangerous (ואין לך ברפואות אלא ספק סכנה).

מפני שכמה פעמים שופך דמים מפני הייאוש ואינו משתדל כראוי במלאכת רפואתו או שאינו יודע לפעמים סבת החולי ודרך רפואתו, ועושה עצמו בקי. בית הבחירה קידושין פ

For often they shed blood, because they give up and do not try to apply their trade as physicians appropriately.  At other times they do not know the etiology of the disease and how it should be treated, and yet pretend as it they do.

Here is a rather different explanation. It is not that medicine is intrinsically worthless (as the Ramban opined), but that physicians are not diligent about how they practice, and do not admit when they are not knowledgeable. Presumably if the physicians were more scrupulous and more honest about the limits of their own knowledge, Meiri would not have them condemned to hell.

In Thomas Dekker’s The Honest Whore, we are told that it is far safer to fight a duel than to consult a doctor. In Ben Johnson’s Volpone doctors are said to be more dangerous than the diseases they treat, for ‘they flay a man / before they kill him’ Trust not the physician;

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His antidotes are poison and he slays.... ~ Shakespeare