Why is hunting big animals more dangerous for the species?
I can see two different sides to this question.

On one side,

From Darwin's Theory of Evolution, the more adapted you are, the better chance at reproducing you will have, thus passing on your genes. 


  "Survival of the fittest" is a phrase that originated from Darwinian
  evolutionary theory as a way of describing the mechanism of natural
  selection. The biological concept of fitness is defined as
  reproductive success.


In this case, you hunt the fittest, strongest animals that can procreate and protect their descendants, leaving the weakest alive. The weakest may not be able to continue the lineage because of their weakest gene pool and the species existence could be at stake.

On the other side,

A reputated Oxford Zoologist, Richard Dawkins wrote: 


  We are survival machines – robot vehicles blindly programmed to
  preserve the selfish molecules known as genes


In this particular example, being strong, fit and healthy could be interpreted as being unfit for evolution, since it attracts predators (humans) to kill, as would not be the case for medium sized less meaty healthy individuals. The true adaptation that could make the specie survive in this case is via the weakest members that are not worth the effort to be hunted but still can survive other threats.

There is several more viewpoints that could be described knowing more details about exactly which animals, their environnement, the other predators and the exact contribution of the "healthy strongest" specimens you described as being hunted.

Nevertheless, hunting animals can always endanger the specie depending on the frequency of the hunt, frequency of the animal reproduction and several other factors, so can many other human behaviors. 

Source: The selfish gene - Richard Dawkins (Book)