The bitter cry for revenge that captures the profound agony of the exiles in Babylon is driven by deep trauma, as they long for a harsh payback that perfectly matches the actions of their destroyers. A sense of praise and honor is directed toward whoever will ultimately step forward to carry out this vengeance against the Babylonian children [מצודת דוד]. The raw emotion of the exiles translates into a desire to see the youngest of their enemies, even nursing infants, shattered and scattered [מצודת ציון].
While this request is incredibly harsh, the primary approach among commentators is that it does not stem from pure cruelty, but rather from the strict principle of measure for measure. The Babylonians had treated the Israelites with terrifying brutality, mercilessly dashing their young children [רד״ק, אבן עזרא] and murdering babies while they were still in their mothers' arms. Because of these horrific acts, the exiles feel the only fitting punishment is a similarly violent death against the rocks. This specific fate is seen as a parallel to stoning, which is considered the most severe of the court-mandated death penalties [אלשיך].
Despite the intensity of this desire for justice, the exiled poet does not want to commit such acts with his own hands. He does not ask for the opportunity to strike the blow himself, but rather hopes that someone else will rise up to deliver the punishment [ביאור שטיינזלץ]. Historically and prophetically, this hope is deeply connected to the foretold destruction of Babylon. It specifically points toward the Medes, who were prophesied to attack Babylon and show absolutely no mercy to the young [מאירי]. This grim wish eventually materialized in the second year of the reign of Cyrus. During that time, he launched a second assault on Babylon, completely destroying the city and bringing an end to its inhabitants [מלבי״ם].