The existing Social Security system could still be left in place for those who are fearful of any kind of private investment. What the privatization of Social Security would do would be to allow others to do otherwise. It is not just individuals who can benefit from the option of privatization. The country as a whole can benefit. One huge difference between private investments and Social Security taxes is that private investments increase the total amount of real wealth and productive capacity in the economy.
Private investments create factories, computer networks, apartment buildings and other real assets.
The money paid into Social Security creates no real assets. It is just more money for politicians in Washington to play around with, leaving it to future administrations and future Congresses to figure out how to take care of future retirees. None of that represents an increase in the nation's real wealth or productive capacity, from which pensioners could be paid. If Social Security produced real assets, like private investments, then we would not have to worry about how many young workers there will be in the future to take care of old pensioners. One of the biggest objections to privatization is ideological.