I will direct your attention to John Calvin's commentary on John 1:29, where Calvin is unable to say anything other than the fact that Christ died for all men -- for the sins of the whole world (although he denied this in his theology):
"Behold the Lamb of God. The principal office of Christ is briefly but clearly stated; that he takes away the sins of the world by the sacrifice of his death, and reconciles men to God. There are other favors, indeed, which Christ bestows upon us, but this is the chief favor, and the rest depend on it; that, by appeasing the wrath of God, he makes us to be reckoned holy and righteous. For from this source flow all the streams of blessings, that, by not imputing our sins, he receives us into favor. Accordingly, John, in order to conduct us to Christ, commences with the gratuitous forgiveness of sins which we obtain through him.
By the word Lamb he alludes to the ancient sacrifices of the Law. He had to do with Jews who, having been accustomed to sacrifices, could not be instructed about atonement for sins in any other way than by holding out to them a sacrifice. As there were various kinds of them, he makes one, by a figure of speech, to stand for the whole; and it is probable that John alluded to the paschal lamb. It must be observed, in general, that John employed this mode of expression, which was better adapted to instruct the Jews, and possessed greater force; as in our own day, in consequence of baptism being generally practiced, we understand better what is meant by obtaining forgiveness of sins through the blood of Christ, when we are told that we are washed and cleansed by it from our pollutions. At the same time, as the Jews commonly held superstitious notions about sacrifices, he corrects this fault in passing, by reminding them of the object to which all the sacrifices were directed...
Who taketh away the sin of the world. He uses the word sin in the singular number, for any kind of iniquity; as if he had said, that every kind of unrighteousness which alienates men from God is taken away by Christ. And when he says, the sin Of The World, he extends this favor indiscriminately to the whole human race; that the Jews might not think that he had been sent to them alone.
But hence we infer that the whole world is involved in the same condemnation; and that as all men without exception are guilty of unrighteousness before God, they need to be reconciled to him. John the Baptist, therefore, by speaking generally of the sin of the world, intended to impress upon us the conviction of our own misery, and to exhort us to seek the remedy. Now our duty is, to embrace the benefit which is offered to all, that each of us may be convinced that there is nothing to hinder him from obtaining reconciliation in Christ, provided that he comes to him by the guidance of faith...
...But John leads us back to Christ alone, and informs us that there is no other way in which God is reconciled to us than through his agency, because he alone takes away sin. He therefore leaves no other refuge for sinners than to flee to Christ; by which he overturns all satisfactions, and purifications, and redemptions, that are invented by men; as, indeed, they are nothing else than base inventions framed by the subtlety of the devil..."
