Assume some form of dualism--whether hylomorphic, substance or property. What is our reason for thinking that non-human animals feel pain? It is presumably that there are situations similar to those that humans find themselves in where animals both exhibit neurological responses similar to human neurological responses correlated with pain and behavioral responses similar to human behavioral responses correlated with pain. Humans in these situations feel pain, and, hence, so do non-human animals that have the same responses.
The argument has the following form: In animals of kind A, states of type C (having such-and-such neurological and behavioral states in the presence of bodily damage) are correlated with states of type D. Therefore, in every kind of animal that can find itself in a state of type C, states of type C are correlated with states of type D. This is in general a pretty weak argument. Consider: "In bats, movements of forelimb muscles are correlated with flying. Therefore, in every kind of animal that can exhibit movements of forelimb muscles, the movements when unimpeded are correlated with flying. (In particular, pigs fly.)" I do not mean that the argument is useless. Suppose that we were alien visitors and having just landed the only animals we were able to observe were bats. We observed that movements of forelimb muscles are correlated with flying. We might well form the working hypothesis that in all other animals, forelimb muscle movements are correlated with flying. But this hypothesis would carry only a little epistemic weight.
Suppose we are still the aliens who have only observed bats. We now notice burrows on the ground. Sonar reveals that the burrows are being made by small animals--moles--that dig lots of tunnels in the ground, and further sonar observation shows that there is sufficient food for them underground. We conclude as a working hypothesis that these animals spend much of their lives underground. Sonar observations suggest that the animals indeed do have forelimbs. But--and I realize this is a bit unlikely--we cannot tell from the sonar whether or not there are wings (they might be folded back over the body). By the earlier working hypothesis we could conclude that if the moles' forelimbs were to move unimpeded (i.e., in an open space), the moles would fly. But this would be unjustified. For given what we have seen of the moles' lifestyle, we see that flying would be of little if any use to them.
Thus, a defeater to generalizing claims of the form "Animals when in state C exhibit D" from one natural kind to another is found when exhibiting D in state C has significant usefulness in the case of the former kind but has little or no usefulness in the case of the latter kind. And if dualism is true, this seems to be how it is in the case of pain. Conscious pain seems to be of no use to non-human animals. One might say that pain is useful for getting an animal to avoid certain situations. But that may well be incorrect in the case of non-human animals: neural states may well be sufficient to cause the behavior of these animals. It seems plausible that if we could do all the impossibly difficult physics calculations, we could predict what the animals will do based their physical states and the states of the environment. But if dualism is true, the pain is something over and beyond the physical states.
Humans have free will and make decisions through a process that goes beyond the physical functioning of the body. Or so at least hylomorphic and substance dualists are going to say. It is plausible that pain--which according to the dualist goes beyond the physical--is needed in order to inform this non-physical process. But this kind of a use won't be there in the case of non-human animals. Moreover, knowledge has non-instrumental value in the case of humans, and the kind of knowledge that pain conveys thus may have non-instrumental value in the case of humans. It does not seem that plausible that this kind of knowledge has much non-instrumental value for non-human animals.
I am not saying animals don't feel pain. I am simply saying that dualists have good reason to find the argument for animals having pain to be evidentially weak.
An objection to the above is that God exists, and we would be deceived in seeing animals apparently feel pain, and God would not allow for such deception. This objection has some force, but we had better not take the claim that God would not allow deception to imply that in all cases of something seeming a certain way, it is in fact that way. We already know that some animal behaviors seem humanlike but in fact have a different significance in non-humans, so we know to be cautious in inferences from humans to other animals. (Interestingly, the deception argument does not apply in the case of animals who lived before human beings came on the scene. Thus, someone impressed by this argument could hold that before the Fall, there was no animal pain.)
As an application, what I have said implies that the argument for the non-existence of God from the evil in animals' suffering pain is quite weak for dualists. It is weak first of all because the argument for animals' suffering pain will be rightly judged weak by dualists. But it is even weaker than that. For the main reason that could remain, after the above arguments, for a dualist to keep on presuming that animals feel pain is that perhaps something of the non-instrumental value that pain has in human life could be there in animals--maybe truth about the state of one's body is innately valuable. But if that is the argument, then the pain is not an evil, at least not in itself.