I agree that, according to passage four, that seemed to be the worry that Cassie had in mind. They were "stealing" the animal's body to do with whatever they wished, and then dismissing it into non-existence whenever they were done with it. (Which is really the same as death, if you are going by this logic.) I think that this is consistent with Cassie's early on beliefs about the spirituality that animals contained.
At that point of time, they had no real idea how morphing worked. Without Ax there to make it somewhat understandable to them what happened (if he ever really could), morphing probably had more of a mystical quality rather than a scientific quality to them, and to Cassie in particular. It is reasonable to assume that she could be worried that they would be stealing the animal's essence more than their DNA, and their temporary inability to control the morph in the beginning would probably reinforce that thought. They are essentially creating animals to just bend them to their will, basically be their slaves.
However, as Rachel said, that is illogical. They merely swapped DNA, didn't create a whole new being. They were still themselves no matter what form they were in. However, in the beginning when they were new to the idea of becoming new creatures, it probably created a strange disassociation in their mind that might have created the belief they were becoming something else. But as the series progressed, they gained a better understanding that they were their morph. But Cassie probably never lost the feeling that they were doing something against nature, humans aren't supposed to be able to 'steal' the bodies of other animals to use it to their aims. Animals were pretty sacred to Cassie, and it probably isn't a large stretch of imagination to imagine her thinking "a wolf would never want this Hork'Bajir dead, what right do I have to use a wolf body to kill it?"
Like Estelore said, I think the more practical worry is using someone's explicit identity to deceive others and use that body for acts that the person who's identity was stolen would not agree with. Most of the other animorphs would agree to that, being humans themselves and understanding the implications, but they didn't extend that courtesy when thinking about animals. To them, animals didn't have identities, but to Cassie they did, and there was no difference between stealing the identity of an animal and the identity of a human.
Still, illogical, (well, perhaps not illogical, but not practical at all when you have the world riding on your shoulders) but I don't think it is so off the mark that she thought that way.