Control
For all his boasts of power, for all he kept his workers in line, Hades knew his control over Hadestown could shatter in an instant. One spark was all it would take to light a fire not even he could put out, and Orpheus's song was everything he feared and more.
He had warned Persephone numerous times about how, were he not exceedingly careful, the kingdom would fall. Giving in a little would make them demand more; letting a tiny crack show would lead it to expand; showing any weakness at all would prove beyond a shadow of a doubt that the inexorable king of the dead could be swayed.
And with Orpheus's song doing all of the above and more—making him laugh and weep just like he'd challenged, making flowers of love bloom from his fingertips—Hades knew that even if he managed to keep his kingdom, his control was slipping away.