Why is Social Security still taking money out each month towards Medicare Part B when I have joined a Medicare Advantage plan?

Yes. Medicare Advantage plans provide care under contract to Medicare. You must continue to pay the monthly Medicare Part B premium when you join a Medicare Advantage plan. You may also have to pay an additional monthly premium to the plan. For the plan premium, the plan may provide benefits like coordination of care or reduce out-of-pocket expenses. If you join a Medicare Advantage plan you are still in the Medicare program and are still entitled to get all your regular Medicare-covered services and have Medicare rights and protections.