It's one thing to have music of lower quality, it's another to be old and dying and watching someone who was born a century before you gifted with youth and vitality. It's not hard to envision that situation if the rich have access to anti-aging.
As such it is a scenario basically based off what science fiction says will happen when anti-aging is available. And people feeling that yes, that is what will happen - which spurs their envy.
The envy of this potential future is an expression of the envy of current disparities in income and power heightened by a fear that the future will make those disparities more unbearable and less fixable than they currently are.