Every American aged 65 or older is eligible for Medicare. Those who receive Social Security benefits are automatically enrolled in Medicare. There is no way to opt out. Either you enroll in Medicare Part A, or you forfeit your Social Security benefits.
There is a great deal of speculation as to why this is, but unfortunately, there is no clear answer. Perhaps this policy was instituted to make it easier for seniors to enroll in Medicare, and was never discontinued when private coverage became more commonplace. Regardless of why, this is the rule, and it is not likely to change in the near future.
Many companies which offer retiree health benefits will terminate your coverage when you turn 65 because they know you have access to Medicare. In this case, even if the government weren't forcing you to choose between Social Security and keeping your private health coverage, your company would be making the decision for you!
But other companies will continue to offer supplemental retiree benefits, which can be used in conjunction with Medicare. These benefits may include prescription drug coverage, doctor visits, and other outpatient health care. Medicare must still be your primary coverage, but you can have private supplemental coverage.