Yes, the inner man is born of the spirit, but we are not just the inner man. We have an old man, too, that hasn't gone anywhere and will be with us until we die.
"Grace" believers don't believe that it's possible to walk in righteousness with a consciousness of their sin nature, and the concomitant imperative to overcome it. Thus they dissociate from what they call
sin-consciousness by considering the flesh and the body to be separate and distinct. In other words, mental separation is made between the flesh and the body, which allows for the belief that the body is sinless. The sinful flesh, then, simply becomes an idea that is compartmentalized in the mind and discarded (ignored, denied) because it is the old man that was crucified and no longer exists. This process of denying the existence of sinful flesh and identifying only with the incorruptible spirit and sinless body is what 'grace' believers call
the renewing of the mind.
The Theological Dictionary of the New Testament has a good description of this mental dissociation process in which a person only identifies with what they want to be (their identity as the righteousness of GOD), and blots out any consciousness or idea contrary to it (their sin nature).
f. Gnosticism offers a radical solution to the conflict of conscience. It is true that instances are very sparse. But the basic dualistic solution involves a full separation between the two egos. The true I of the Gnostic is identical with the divine world of light, while the other I belongs to the chaotic world and is thus to be abandoned. In the final analysis, then, there is no bad conscience for the Gnostic. Naturally this opens the door not merely to asceticism but also to libertinism.
Paul talks about the two 'I's mentioned above in Romans 7-8, in which victory is found, not through denial of the sinful flesh's existence, but through not obeying it in grace through faith.