Why does a progressive tax code produce a retirement annuity for a middle-class household that is similar

Question:

Why does a progressive tax code produce a retirement for a middle-class household that is similar to that which would follow from a flat tax?
Annuity
An annuity is a series of equal payment made at equal intervals during a period of time. In other words annuity is a contract between insurer and insurance company in which insurer make a lump-sum payment or a series of payment and, in return,...