Intellection, however, is not reducible to a material operation. I don’t know that I want to do a full write-up, but to clarify, St. Thomas did not equate intellection to consciousness. A unified sensory experience, perception (including the “qualia” the rationalists made such a big deal of), memory, the ability to estimate, even imagination are considered entirely reducible to material operations as each of these concerns the particular. Even emotions are material operations, not immaterial. St. Thomas attributes all of these things to animals and holds that these material powers play an important role in our own consciousness. Intellection refers specifically to what is not particular. It refers to the universal form abstracted from all particularizing features, abstracted from material conditions. This is the ability of rational animals to grasp universals after experiencing particular things, and this allows for things such as our conceptual language, philosophy, etc… Since intellection is not reducible to material operations, it therefore is an immaterial operation, and what is immaterial is not corruptible. It has no tendency to decay, it has no tendency to come apart. Therefore, even when material operations cease in rational animals the immaterial operations do not, and since the operations persist so does the form (soul) of which they are a power of.
A few more points of clarification, as I said, the material operations cease. The material processes of memory, estimation, sensation, imagination cease after death (or at least they would naturally do so, whether God provides some type of additional support isn’t a question answerable by natural theology). What persists is only the operations of intellection (without any sensory input or change, just the sum total impressions, knowledge, and a direction of the will that doesn’t get any new info or competing appetites). Apart from the body (or divine intervention) we become pretty handicapped beings. Immortal, in that there is persistence, but we lose most of the operations that naturally follow from being human. It’s just this one little facet of operations/properties that don’t decay. We reject any Platonic or Cartesian idea of the soul being ‘what we really are’ and the body just a machine. We are not complete without the soul as the form of a body. And hylemorphism rejects the notion of the soul as an additional vital principle to the formal principle (which is something all material substances have, alive or not) and prime matter. Thomists argue about whether what remains after death can even be called a human being (even if it is a human soul) or a substance in itself.
But anyway, what distinguishes the form of a human being from the form of a rose or the form of a dog is that a human being has properties which point to immaterial operations, whereas roses and dogs have properties entirely explainable by material operations. And what is immaterial is not corruptible (in the sense of a tendency to decay or towards ceasing to exist).