Why would a person enter the Communion line but not receive Communion?

For the first time I can remember I saw a little girl at Mass go up for Communion but cross her arms over her chest. What does the priest say to this individual?

The posture of approaching the priest with arms crossed over the chest is commonly understood to be a request for a blessing rather than for Communion. I suspect that the child you saw was too young for Communion and her parents had taught her how to request a blessing instead. The priest gives a blessing to a person who approaches him this way.

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