The libertarian mystery (if there is one) would not involve an explicit or implicit contradiction. It would merely be an admission that there is a limit to how much man can know about the nature of a free choice.
In a less obvious way, determinism could be said to lack livability. How does one live as though all of his actions and thoughts are determined?
As a signer of the Traditionalist Statement on Baptist Soteriology, I affirm that one result of the fall is that man inherits a nature and environment inclined toward sin.