I personally find this idea immensely disturbing. I feel this has the potential to lead to animal cruelty and I feel people who believe this don't fully understand the implications of this view.
For example, the biblical teaching is that the soul is the mind. If you have no soul, "you" as a being do not exist. Saying animals lack a soul is essentially saying that they are robots. They would just have physical reactions, like the AI program "Cleverbot" (which means dogs really have no more value than plants or bacteria).
If you say animals lack souls but are conscious beings that can have experiences, you are saying that the mind can emerge through purely natural processes. That's fine for an atheist but most Christians would reject it. So, which is it?
Sure, this is a common view throughout the ages, but as I have discussed before, that does not matter. What matters is if there is any biblical precedent for the view. The church has historically held views that were wrong. In my opinion, saying "this has been the historical christian view" is an "appeal to authority" fallacy.
In fact, both Hebrew words for "soul" (Nefesh and Ruakh) are used many times in reference to animals. See here and here.
I really see no philosophical or biblical justification for animals having no souls, and I see many reasons to think that they do have souls. If you have a good reason, feel free to drop me an email.
Perhaps a more debated question is whether or not animals have afterlives, but even this is not stated in scripture. The only verse I have heard quoted to "prove" that animals do not have an afterlife is Ecclesiastes 3:20-22 "All go to one place. All are from the dust, and to dust all return. Who knows whether the spirit of man goes upward and the spirit of the beast goes down into the earth?" but this still seems like an extremely weak argument to me. Solomon is lamenting that he doesn't know what happens to the soul after death. He does not make the claim that animal souls "die" after physical death.
I once read an article that presented "what about sea life, what about dinosaurs, what about trilobites?" as an argument against animal afterlives. To which I would respond with "so what?". Why can't all dead animals have an afterlife. Is heaven going to be too small to fit all of them? The conclusion of this argument does not follow from the premises in any clear way.
If you believe animals have no afterlife, I have a few points to raise:
1. It seems unbiblical to take the view that animals simply do not have souls. So, I would ask, how does the soul of an animal "die"? Matthew 10:28 "And do not fear those who kill the body but cannot kill the soul. Rather fear him who can destroy both soul and body in hell." seems to imply that only God can destroy a soul. So, does God destroy the soul of animals when they die? Why would that be?
2. Why should a human life have any higher value than an animal life in this case? I would value animal lives more than humans if this were true, because they are gone forever upon physical death, whereas humans live on for eternity.
Personally, I feel that God will give every passed animal a happy and eternal afterlife. I even have some scriptural precedent for it, unlike the opposing positions. One of which is Isaiah, who speaks of many animals on the new heavens and earth (or the millennium, depending on your interpretation of the passage).
You could take the view that after the apocalypse, God re-creates new animals of the same species as the old ones. But nowhere does any prophecy state this. The prophecies do speak of a resurrection in which humans are revived. It seems reasonable that these animals are another product of that resurrection. (And no, they could not have survived the apocalypse, the seven bowl judgements are far too severe for any animal life to survive)
Some have taken this passage as allegory or metaphor. But this is a problem I have with many prophecy teachers (*cough* amillennialists and preterists *cough* *cough*), they take passages metaphorically for no obvious reason. And "cherry-pick" which passages to take literally. Unless you can give me a legitimate reason to take this passage metaphorically, a literal reading is the best bet.
So, do animals have souls? Definitely!
Do animals have an afterlife? Probably, in my opinion.
Thanks for reading!