This also belong to philosophy, so we will have ask for their help to get answer to this question.
This article deals with human life value, but also covers animals value:
What is it about human life that makes it valuable?
I can think of two plausible candidates: (a) consciousness, and (b) a
holistic relation of our bodies and consciousness.
Do all animals have value?
If it is consciousness (or even an embodied consciousness) that has value, then it seems very likely that other animals also have value because it’s pretty obvious that other animals also have minds.
Animal consciousness is confirmed by various studies and is summed up on this Wikipedia article:
In 2012, a group of neuroscientists signed the Cambridge Declaration
on Consciousness, which "unequivocally" asserted that "humans are not
unique in possessing the neurological substrates that generate
consciousness. Non-human animals, including all mammals and birds, and
many other creatures, including octopuses, also possess these neural
So, there seem to be no special difference between us humans and other animals.
A similar question was put on Philosophy SE site and it received a very interesting answer:
I think we should avoid a moral basis in absolute human value, which
seems to me to culminate in the tradition of trophy hunting, where
human comfort and enjoyment is of value, and the lives of animals hold
little intrinsic value. Instead, we should look at the agreements
'negotiated' by our societies and our genes, and consider where
everyone's best interests lie, but accept that we will always value
those more like ourselves higher than others to some degree.
Of course, that's not a definite answer (it's philosophy, after all, much more questions than answers), but it leads us to the idea that humans might have more intrinsic values.
This article tells us about various intrinsic value of humans. I think that some of them do not apply to animals. E.g.:
- Moral nihilism - None
- Humanism - human flourishing
- Rational deontologism virtue or duty
Conclusion: Animals have intrinsic value (at least consciousness that has been studied for quite a while), but humans seem to have more.
One scenario I can imagine can deny intrinsic value of animals is denying that they possess consciousnesses, but as already mentioned, this is very unlikely.
I will try to improve the answer, but I cannot provide a definitive answer. I also think that such an answer is next to impossible to find, as proof of impossibility is usually much harder to find even in exact sciences:
To prove that something is impossible is usually much harder than the
opposite task; it is necessary to develop a theory
Also, some believe that proving a negative (evidence of absence) cannot be done:
In 1992 during a presentation at Caltech, skeptic James Randi said
"you can't prove a negative". He claims that it is impossible to
'prove' a negative assertion (such as 'telepathy does not exist').
Coming back to your question. I will try to make it more answerable by narrowing and getting it closer to vegetarianism: what human intrinsic values that seem absent in animals also entitle humans to hunt/kill/eat animals?
I am going to use convenient items from the list of intrinsic values:
- Hedonism - pleasure - entitles human to hunt for pleasure
- Utilitarianism - utility - allow humans to kill and eat animals because they need it to get high quality proteins