An "objective unbeliever"? That, my friend, is a creature of myth, a conceptual oxymoron. And this was precisely Paul's point to the Corinithians.
In view of the humility (2:1-5) and veracity (2:6-13) of Paul's message, why did some among them still reject his teaching? Because they did not want to accept it. The rejecters do not, in fact, "accept" (dechetai) his message, which is to say that they do not welcome or receive the message as one would a guest. So it is not that the unbeliever "cannot understand" the message because "Jesus Christ, and Him crucified" (v. 2) is irrational and overly complex... it is because He is not welcome.
Given a wrong inclination, wrong volitions must follow. If the disposition of the will be vicious, the volitions of the will cannot be virtuous, any more than the fruit can be grapes if the root is that of the thistle.- William Shedd, Dogmatic Theology, 4.5.
It is because the news of Jesus is not welcome that men "cannot understand" or mock Him as "foolishness." Fallen humanity is not lacking in bare ability, it is that they have no desire. Man's rejection is so hostile that it may be described as total inability.
This principle of irrationality by rejection also carries a rather searching application to those of us whose desire has been mercifully changed by God's Spirit, but for whom sin remains an experiential reality... do you yourself welcome the truth as a long-awaited guest?