Private social security accounts

There is a lot of back and forth concerning private social security accounts. The preliminary talk is that they will be investment accounts that can be used to create income in retirement and also willable to heirs on the death of the holder. The question I have is why do those who are opposed to these accounts not want you and I to have an account that we can call our own? This is our own money after all, why can't we create an account that will grow over time and either support us when we retire or be willed to our heirs? When my Mother died, after having paid ?thousands of dollars into social security, her heirs got $250. I recommend, regardless of your views on this subject, to go to this site, http://www.daveramsey.com/, click on the Social Security Reform 'button' and calculate what you would be able to save under this private account.