John Lightfoot on Matthew 19:13

[Then were little children brought unto him.] Not for the healing of some disease; for if this had been the end propounded, why did the disciples keep them back above all others, or chide any for their access? Nor can we believe that they were the children of unbelieving Jews, when it is scarcely probable that they, despising the doctrine and person of Christ, would desire his blessing. Some therefore of those that believe brought their infants to Christ, that he might take particular notice of them, and admit them into his discipleship, and mark them for his by his blessing. Perhaps the disciples thought this an excess of officious religion; or that they would be too troublesome to their Master; and hence they opposed them: but Christ countenanceth the same thing, and favours again that doctrine which he had laid down, chapter 18:3; namely, that the infants of believers were as much disciples and partakers of the kingdom of heaven as their parents.