Your money is not ever saved for you. Your retirement is NOT funded by your own past taxes. Your retirement is funded by those younger people who are then working and paying taxes.
You can see the details at https://en.wikipedia.org/wiki/Social_Security_Trust_Fund
Payments to retirees are made out of _currently incoming funds_. That is, the money paid in taxes by people currently working is immediately distributed to retired people who are receiving Social Security payments.
It is, in other words, NOT a savings plan. Full stop.
This scheme sort of worked in the 1930s when life expectancies were much lower and only a few people survived to retirement age relative to the much larger number of working people paying taxes.
Since 2009, Social Security has operated at an annual loss: the amount paid out has begun to exceed the incoming taxes. The deficit is expected to increase a lot in the coming years. (See https://www.cbo.gov/sites/default/files/cbofiles/attachments...)
Whatever you may think about whether Social Security is a good idea or whether the goverment ought to provide for retirement, it's clear that the current structure is not going to do that for much longer. A large-scale reform of some kind is coming.