Your point is interesting. Would not animals then be spiritual? as we can plainly see that animals have the breath of life in them. The breath of life would also had to have been blown into a bloody nose, as Scripture clearly states that the soul is in the blood. This is why the children of God must obstain from the consumption of blood, because the life is in the blood.
My current understanding is is that our minds are essentially who we are, or our spirit's. The soul is the process of oxygenation of the blood, which sustains life and therefore our bodies,giving us our being. Our bodies have a brain made of flesh. This is what Satan is lord over, currently. We are here to choose which lord we desire, the lord of flesh, or The Lord of the mind or spirit.
Satan was also lord of the flesh before God stepped in and made a better one. This is why the serpent wanted his fall. In fact this instance in the garden is when he lost his birthright as lord of the physical. But be as it always is with the Lord of hosts, righteousness must always prevail. It was then that our Lord agreed to offer himself to His Father as a blood sacrifice, for He so loved the world as much as His Father did, and does.
It is true that we are made of the dust, and of course Science got it right again. But God is telling us much more than this in the underlying ambiguity. Satan was before and at the time of the birth of Adam, the lord of the world. Lord of the dust. Lord of that which dies.