This myth often comes from a mis-understanding of specific terminology - differentiating between the terms ‘Vegetarian/Vegan’ and ‘Plant-Based’. Once we have a clearer understanding of these two terms, and the difference between them, then it’s quite easy to move past this mis-conception.
It is common nowadays to see or hear the recommendation to follow a ‘plant-based’ diet for a myriad of reasons, from health to sustainability (a topic for another day), but often we assume that a ‘plant-based’ diet means a diet absent of meat or fish - a vegetarian, or even vegan, diet. However, this is simply not the case. By definition, a ‘plant-based’ diet is simply a diet where the majority (read: more than 50%) of our food and calorie intake comes from plants… which, as you can imagine, is vastly different from a fully vegetarian approach. Now, is a plant-based diet (under this definition) going to better for your health? In most circumstances, yes.
However, it is still possible to eat food from animal sources and still follow a plant-based diet - some people might tell you that’s wrong, but by definition it is wholly possible. Following a plant-based diet may mean reducing the amount of meat and food from animal sources that you have, but it doesn’t require you to eliminate them entirely. Let me be very clear: food from animal sources is absolutely not bad for your health.
Now, this is not to say that vegetarian or vegan diets are inferior to a meat-eating diet, but we need to be careful about claiming their superiority to other dietary approaches. What the current evidence shows is that, when calorie controlled, there is very little difference between a good quality vegetarian diet and a good quality meat-eating diet. There is very little difference in relative or absolute risk of developing illness or disease, and their health benefits are very comparable.
Obviously, if we compare a high-quality vegetarian diet with a low-quality ‘western diet’ (or vice versa), then the results are going to be vastly different - which is why, as we always say, it is not about the particular dietary approach, but the application of each approach that is important.
Vegetarians and vegans can actually be more likely to develop micronutrient deficiencies due to the restrictive nature of their diets. Some minerals, such as iron, are found in very high amounts in meat products (red meat for example), but in much smaller amounts in plant-based sources. This naturally makes it tougher for vegetarians and vegans to meet all of their micronutrient requirements. For that reason, it can sometimes be necessary for vegetarians or vegans to supplement certain nutrients (though this is very dependant on each individual).
Ultimately, it’s another case of ‘don’t believe the hype’ - vegetarian and vegan diets can be extremely healthy, but no healthier than an equivalent meat-eating diet. When it comes to our own health, the overall complexion of our diet is what really matters.