All of us, therefore, descending from an impure seed, come into the world tainted with the contagion of sin. Nay, before we behold the light of the sun we are in God's sight defiled and polluted.... But if... the righteousness of Christ, and thereby life, is our by communication, it follows that both of these were lost in Adam that they might be recovered in Christ, whereas sin and death were brought in by Adam, that they might be abolished in Christ. There is no obscurity in the words "As by one man's disobedience many were made sinners, so by the obedience of one shall many be made righteous." Accordingly, the relation subsisting between the two is this: As Adam, by his ruin, involved and ruined us, so Christ, by his grace, restored us to salvation. (Calvin, Institutes, II.i.5-6)In other words, to believe that we are objectively free to choose good or evil is to strip the Cross of its power and to make it a mere example. But to believe that we are bound in sin by nature is to believe that we are freed from sin by Christ's work of atonement.
I'm not sure this is a convincing argument for original sin, but I think at least it's an interesting one.