I don't think they're saying it's unhealthy to eat meat. I believe they're asking whether people in Renaissance Europe may have thought that meat was unhealthy.

People in pre-modern societies did, in fact, have their own various ideas about healthy eating. Some of these ideas were not "correct," necessarily, from a modern perspective. For example, during the Middle Ages (to my knowledge), it was widely believed that food should be consumed in certain orders, and in certain combinations, to improve digestion. This was based on the "four humors" idea, with foods organized by hot vs cold and moist vs dry.

There are also traditions from India that classify certain foods as healthy or unhealthy, often in a way that might not hold up to modern scientific scrutiny. For example, there's a tradition within Hinduism of considering foods to be either Sattvic, Rajic, or Tamasic. Tamasic foods are considered to have a sedative effect on the body, and are often avoided. This can include things like meat and Alium species. There are sects that actually avoid these foods, even though we tend to think of Indian food as being full of garlic, onion, and other spices.

Are any of those things "really" unhealthy? No, but these dietetic beliefs are based on older philosophical systems, not on modern empirical medical science.

I am not a historian.