Following the destruction of Jerusalem, the Babylonian exiles faced not only the deep pain of being uprooted from their home but also a cruel demand from their captors. This harsh interaction explains exactly why the grieving Israelites felt compelled to silence their musical instruments. The Babylonians approached the exiles and demanded that they sing. This request stemmed either from a simple curiosity to hear the famous melodies of the Israelites or from a cynical desire to mock and abuse the broken captives [ביאור שטיינזלץ]. Observing the immense grief of the exiles, the captors might have initially asked only to hear the spoken lyrics of the songs, without the actual music [אלשיך]. Another perspective suggests a more defiant motive: the captors wanted the exiles to take their traditional songs of praise for Jerusalem and sing them instead about Babylon, forcing them to accept Babylon as their new homeland [מלבי״ם].
The nature of these captors adds layers to the cruelty of the situation. The primary approach among commentators is that these enemies were either mockers reveling in the pain of the exiles [רש״י, מצודת ציון, מצודת דוד], or the very plunderers who had just robbed them [ביאור שטיינזלץ, מלבי״ם]. Taking a different approach, some explain that the captors noticed the exiles had not destroyed their harps but had merely hung them on the trees. To the Babylonians, this preservation of the instruments was a sign that the exiles still held onto a spark of hope and joy. Consequently, they demanded that the Israelites take down those hanging instruments, rejoice, and play them [רש״י, רד״ק, אלשיך].
Conversely, another view highlights the sheer cruelty of the moment by contrasting the exiles' sorrow with the captors' demands. Right in the midst of the Israelites' bitter wailing and sighing, the captors demanded a display of joy [רד״ק, מאירי]. Ultimately, the captors specifically asked for a song of Zion. They were not asking for ordinary music, but rather for the magnificent, holy songs that were once performed in the Temple [ביאור שטיינזלץ].