The Temple was Israel's central place of worship, and the children's cry 'Hosanna to the Son of David' is messianic royal praise. The chief priests and scribes regard the acclamation as objectionable enough to challenge Jesus.
Jesus does not silence the children. Instead, he appeals to Scripture to justify what is occurring.
Psalm 8 is addressed to the LORD and celebrates the majesty of God's name throughout the earth. Verse 2 speaks of praise or strength established from the mouths of children and infants.
By citing this psalm in defense of praise being offered to himself, Jesus draws a striking connection between the scriptural praise of God and the acclamation he receives.
After cleansing the Temple and healing the blind and lame there, Jesus is praised by children crying, 'Hosanna to the Son of David.' The religious leaders become indignant and ask whether Jesus hears what they are saying.
Jesus answers yes and quotes Psalm 8. Rather than correcting the children for misdirected devotion, he provides biblical warrant for their praise.
The children's messianic title alone does not amount to a declaration of deity, and the scene should not be exaggerated.
Its strong Christological force lies in Jesus' response: a psalm concerning praise established for the LORD is invoked to defend praise directed toward Jesus in God's Temple. This coheres with Matthew's broader pattern of Jesus receiving worship.
The chief priests and scribes are indignant at the children's praise; Jesus explicitly defends it from Scripture.