I work for UPS and I always wondered if I pay FICA, then why do I have to pay FICA Medicare?

Realistically, you are paying FICA to provide Social Security checks to citizens over 65 or so (depending on when they start to draw it, could be 62). Also, there are many other SSI programs such as disability.
And the Medicare deduction pays for health insurance for those over 65.
The employee pays at each pay day for these items too.

FICA is a terms that generally refers to BOTH Social Security and Medicare taxes TOGETHER.

Your company apparently puts the term on the pay stubs with Social Security and Medicare entries, which MUST be listed separately because Social Security has a cap of $104K, while Medicare has NO cap at all.