Question

Why do most people object to the idea of using a price system to allocate organs rather than the current donation system and first-come, first served system?

Answer 1

A price system to allocate the organs will make the poor very vulnerable.

As organ receivers: Poor will not be able to receive organs no matter how much they need it. People with deeper pockets will get all the benefit. The supply or donation of organs is limited but the people who need it is much more. This demand and supply mismatch will help rich as they are the only who can pay more and more amount for organs leaving poor in a vulnerable situation.  

As organ donation: If a price is set up for organs, people who don't have much money might try to sell their organ to other people who are paying for it. Right now organ donation is seen as a benevolent act where a person donates only when he wants to help. Putting a price will encourage the poor to give up their organs and live a miserable life.