Mortality doesn't cause people to sin. That's like saying longevity causes people stay healthy... longevity doesn't cause people to be healthy any more than mortality causes people to sin. Romans 5:12 says that sin leads to death but grace leads to eternal life.
actually, Rom 5:12 states that Adam's sin led to the condemnation of death. It that death that is hereditary, is passed on by birth which is why we are all mortals.
Rom 5:21 states emphatically that sin is due to death. As does I Cor 15:56. It is the primary reason why Christ came, to defeat death and sin. Both are tools of the devil, Heb 2:14, I John 38. Christ died with our mortal nature so that by His resurrection He gave life to the world and mankind. It is why believers have always believed in the resurrection of the dead.
You have no text that can refute this from scripture without twisting the meaning to support some errant view.
Such texts as Rom 5:18, I Cor 15:12-22, II Tim 1:10, Heb 2:9 all state that death is what Christ defeated. We mortals sin so easily because of our mortal nature. There is nothing in scripture to change it to something else outside of false teachings of men, such as Augustine and many others that followed.
Your statement of sin leads to death, post Adam's fall, only applies to spiritual death. And spiritual death or eternal life the opposite could not even take place except that Christ defeated Satan's power of death.
