The fundamental quality that makes science scientific is empiricism. Math is a purely rational discipline, almost the definition of such. It may be perfectly internally consistent, but it involves no empirical confirmation against external reality.

It is slightly alarming that someone teaching at the university level seems to be lacking an understanding of the basic philosophical assumptions behind scientific reasoning. Although, in my experience, this is hardly an anomaly. These days, to most, science has become just a collection of facts...

No need to invoke epinephrine ("adrenaline") here, nor "DNA damage". Another stress hormone, cortisol, is already well understood to be the major link between stress and adverse health effects.

This is a basic is/ought fallacy. Here is an essay I wrote on the topic a while back:

Diet: Past and Future

One of the most common arguments one encounters when discussing vegetarianism is that our bodies are designed for eating meat, therefore we should continue to eat meat. The usual response to this by vegetarians is to deny that the human body is adapted to eat meat. The latter argument, in fact, was used by Mahatma Gandhi to support his belief in vegetarianism. He compared the human digestive tract to that of various carnivores and herbivores, based on things such as length of the intestines and acidity of the stomach, and came to the conclusion that humans were herbivores. Gandhi was a brilliant man, but he was a lawyer, not a biologist.

It is easy to argue either of these positions, by picking and choosing specific aspects of our digestive tract. The reality is that our bodies are designed to survive on an omnivorous diet. We have adaptations for digesting a plant based diet, as well as very specific adaptations for digesting meat. An irrefutable example of one of these adaptations is the fact that we have transporters in the wall of our small intestine that allow us to absorb heme iron very efficiently. Heme iron only occurs in animal tissues, as hemoglobin in the blood and myoglobin in muscles. These transporters are very specific, in that they will only absorb heme iron, and not the inorganic iron that occurs in plants. The only reason they could have evolved is to absorb the iron from meat in our diets.

Arguing whether or not we should eat meat on the basis of our digestive adaptations completely misrepresents the issue at hand. These adaptations have arisen over millions of years of evolution, and they reflect the selective pressures of a distant past. Certainly in the time of hunter-gatherer societies it would have been near impossible to get enough calories or protein in one's diet to survive without consuming meat. However, with the current abundance and variety of food available to us, it is easy to live on a vegetarian or even vegan diet. The key issue then, is one of choice. Modern humans can live on either a plant-centred or animal-centred diet. The choice is up to us, to decide on our own ethical grounds. Taking into account the environmental impact of our food choices, among other factors, the decision is clear. Humans may have survived the past by eating meat, but a plant-centred diet is the way to a sustainable future.