I would say Key was being too extensive in their analysis. Animals are more complex carbon based lifeforms than plants, particular in that unlike plants and fungi in particular, animals can clearly feel pain. Humans, like animals, can feel pain and have similar physical senses, albeit less than a cat or a dog's sense of smell or sight.
When a Christian, like Aquinas or even Augustine from what I remember, says we are animals, that is not to devalue them, it's only to reflect a relation we have to animals. We are like animals, we are not the same as animals.
And it would be counterproductive for a humanist in any sense, secular or otherwise, to devalue humans in comparing them to animals. Again, the comparison by even a secular humanist of humans to animals is not a matter of univocation or equivocation. We are analogous to animals in sharing many qualities, though obviously in this analogy we admit animals lack certain qualities humans do, like complex brain activity and the ability to make varied judgments, and more relevant nowadays, to multitask, lol.