See also: Brain imaging spots our abstract choices before we do:
If we do not have free will, in the sense of being able to make choices apart from natural processes in our brain; we cannot be accountable to God. Adam could not be held responsible for his "sin." The punishment by God of all mankind was unjust; because Adam had no independent control over the natural processes in his own brain. Those processes would have been created and set in motion by God himself. Therefore God alone would be responsible for the sin of Adam.
For Christadelphianism to make sense, we have to have fee will. But science indicates that our free will is merely an illusion.