"Therefore whoever eats the bread or drinks the cup of the Lord in an unworthy manner, shall be guilty of the body and the blood of the Lord. But a man must examine himself, and in so doing he is to eat of the bread and drink of the cup."
Since smaller children are unable to "examine themselves", it is argued, it is not appropriate for them to take communion. This argument dissolves when the passage is examined in context, which I shall attempt to do now.
The apostle Paul is not happy with the Corinthians. They are supposed to be a united church, but instead "divisions exist" amongst them (v18). This is particularly evident in the way in which communion is 'celebrated':
"in your eating each one takes his own supper first; and one is hungry and another is drunk. What! Do you not have houses in which to eat and drink? Or do you despise the church of God and shame those who have nothing?" (v21-22)
Paul is appalled at their behaviour, particularly noting how the rich believers are unwilling to share their food with the poor believers, shaming "those who have nothing". This is the context in which to understand his instruction in verses 27-28. A believer must "examine himself" before taking the supper in order to ensure that he is judging the body rightly (v29). By "the body" Paul means the church, he is instructing the believers to ensure that they do not exclude other members of the congregation from the supper.
So should small children be permitted to take the Lord's supper? Absolutely! To refuse them the supper would be to exclude them, which would go completely against the apostle Paul's instructions in 1 Corinthians 11. I conclude with the words of Christ:
"Permit the children to come to Me; do not hinder them; for the kingdom of God belongs to such as these. "Truly I say to you, whoever does not receive the kingdom of God like a child will not enter it at all." (Mark 13:14-15)