I, personally, reject your argument. I think (and the CCC backs this up) that for someone to designate their organs to be donated to prolong a life when their own is over is a hugely generous thing to do. One of my sisters received an organ that saved her life. She would be dead about 12 years now without the organ transplantation.
Your argument that it is unnatural is wrong. The tissue being transplanted is being used as it was intended, though in a body other than the original. By your argument, blood transfusions should also be prohibited by the church. Perhaps you agree with Jehovah’s Witnesses on this?

If so, what else that goes against Church teaching do you promote?
Selfless giving and compassion are never condemned by the Church, not even in the case of organ donation. I would suggest you open your heart AND mind a little.