John Calvin writes in the Institutes about the possibility of admitting children to the Lord’s Supper by virtue of their baptism once and only once:

At length they object, that there is not greater reason for admitting infants to baptism than to the Lord’s Supper, to which, however, they are never admitted: as if Scripture did not in every way draw a wide distinction between them. In the early Church, indeed, the Lord’s Supper was frequently given to infants, as appears from Cyprian and Augustine, (August. ad Bonif. Lib. 1;) but the practice justly became obsolete. For if we attend to the peculiar nature of baptism, it is a kind of entrance, and as it were initiation into the Church, by which we are ranked among the people of God, a sign of our spiritual regeneration, by which we are again born to be children of God, whereas on the contrary the Supper is intended for those of riper years, who, having passed the tender period of infancy, are fit to bear solid food.This distinction is very clearly pointed out in Scripture. For there, as far as regards baptism, the Lord makes no selection of age, whereas he does not admit all to partake of the Supper, but confines it to those who are fit to discern the body and blood of the Lord, to examine their own conscience, to show forth the Lord’s death, and understand its power. Can we wish anything clearer than what the apostle says, when he thus exhorts, “Let a man examine himself, and so let him eat of that bread, and drink of that cup?” (1 Cor. 11: 28.) Examination, therefore, must precede, and this it were vain to expect from infants. Again, “He that eateth and drinketh unworthily, eateth and drinketh damnation to himself, not discerning the Lord’s body.” If they cannot partake worthily without being able duly to discern the sanctity of the Lord’s body, why should we stretch out poison to our young children instead of vivifying food? Then what is our Lord’s injunction? “Do this in remembrance of me.” And what the inference which the apostle draws from this? “As often as ye eat this bread, and drink this cup, ye do show the Lord’s death till he come.” How, pray, can we require infants to commemorate any event of which they have no understanding; how require them to “show forth the Lord’s death,” of the nature and benefit of which they have no idea? Nothing of the kind is prescribed by baptism. Wherefore, there is the greatest difference between the two signs. This also we observe in similar signs under the old dispensation. Circumcision, which, as is well known, corresponds to our baptism, was intended for infants, but the Passover, for which the Supper is substituted, did not admit all kinds of guests promiscuously, but was duly eaten only by those who were of an age sufficient to ask the meaning of it, (Exod. 12: 26.) Had these men the least particle of soundness in their brain, would they be thus blind as to a matter so very clear and obvious?” (Institutes of the Christian Religion, Book 4, Chapter 16, Section 30)

So wrote John Calvin. Why are so many people in the Reformed heritage finding themselves in disagreement with him?

• The first thing to note is that Calvin is not responding to a Reformed paedocommunionist. To claim that Calvin condemned paedocommunion is simply not the case. He condemned Anabaptists who postulated paedocommunion as a way of defeating arguments for paedobaptism. If Calvin was interacting with, say, Martin Bucer, or Melanchthon, or even commenting on John Huss and described one of them in such vitriolic terms, then anti-paedocommunionists would have some justification for condemning G. I. Williamson or Dr. Robert Rayburn with such vehemence .As it is, the fact remains that paedocommunion received no serious consideration at the time of the Reformation so that we heirs of the Reformation have any prima facie reason not to reconsider the tradition we inherited from the medieval Roman Catholic Church. John Calvin and Martin Luther and many others had grown up with a certain sort of practice as well as a rationalization for that practice that appealed to Scripture. They were not in the position of John Huss and his followers, over a century earlier and farther east, who still remembered that at one time children had been given access to the Communion Meal and then later barred.Thus, the simple fact that Calvin took the same basic line as the medieval schoolmen on this issue simply does not hold much weight of itself. If his Scriptural arguments are good, then his position is sound, but his mere opinion is not of much help in defining orthodoxy at this point.
• A second thing to notice is that the first of the two paragraphs quoted above contains no argument at all but is simply an assertion of Calvin’s position.Calvin’s assertion about the “requirement” to discern the Lord’s body simply begs the question. Why assume such a requirement is placed on infants or toddlers? He has already dealt with passages which state that one must repent before being baptized and that one must work in order to eat. Why are these passages not applied to infants? Baptists in fact do apply exhortations to repent and believe to infants. Since infants cannot consciously believe in the way that older people can, they reason that infants are not to be baptized. Calvin’s argument here would require him to agree with credobaptism. Obviously, Calvin really didn’t have any reformed paedobaptists to deal with. He was simply snapping at Anabaptist enemies and felt no need to take them seriously.
• Calvin’s text to support the notion that children did not partake of Passover is completely inadequate for the task that he wants it to perform. The text only tells parents what to answer their children when they as about Passover. It says nothing about this being a catechism that they must master before they partake (as some have recently asserted). What sort of catechism is it in which the children ask the question and the parents answer? Nor does the text even give any indication that this question is to be asked at the Passover meal. All it says is that when a child asks, the parents are supposed to give a certain answer. Nothing is said about the child reaching a certain level of understanding before being permitted to participate.
• It is important to note that God is careful to tell Moses who should be restricted from partaking the Passover: those who have not been circumcised. If there were any additional classes of persons who should not be permitted to eat of the meal one would expect God to actually bother to say something about it. God says that the meal is only for the circumcised. Calvin says that young circumcised males were also prohibited from participation but he gives no text for this prohibition. Is this not a good reason to wonder whether God is pleased with us in following Calvin on this matter? As great as Calvin was shouldn’t we be following God in this case?
• It is interesting to note that modern anti-paedocommunionists quite commonly now claim that it is a distinctively paedocommunionist error to tie the Lord’s Supper to Passover (Leonard Coppes, for example). Yes, they say, Passover was for children by virtue of their membership in God’s covenant people, but the Lord’s Supper is different. One can only be amazed at how strained their new interpretions are and how they implicitly admit that Calvin’s reasoning means he should have been a paedocommunionist. This again should give one reason to reconsider Calvin’s stance on the matter.
• In light of the above defects in Calvin’s argumentation and the resulting shifts that have occurred among those who wish to find some way to maintain his conclusion, John Murray’s statement on the issue is quite interesting:
  

  It is objected that paedobaptists are strangely inconsistent in dispensing baptism to infants and yet refusing to admit them to the Lord’s able … At the outset it should be admitted that if paedobaptists are inconsistent in this discrimination, then the relinquishment of infant baptism is not the only way of resolving the inconsistency. It could be resolved by going in the other direction, namely, that of admitting infants to the Lord’s Supper. And when all factors entering into this dispute are taken into account, particularly the principle involved in infant baptism, then far less would be at stake in admitting infants to the Lord’s Supper than would be at stake in abandoning infant baptism. This will serve to point up the significance of infant baptism in the divine economy of grace [Christian Baptism (Phillipsburg, NJ: Presbyterian and Reformed Publishing Company, 1980). pp. 73-74].

Other reasons could be added, but this hopefully will give readers initial reasons why they should reconsider Calvin’s position on the issue, and why doing so need not constitute a rejection of the entire legacy of the great Reformer. Surely Calvin would want his intellectual heirs to follow what Jesus tells us in the Bible rather than his own writings.