Government subsidizes health care services and medicine. By putting more money towards those services and medicine, the sellers of such products and services can raise their prices.
Supply/Demand. You are artificially increasing the amount of demand while the supply increases slower. That = price increases.
Unfortunately, we're in a place where every time the price goes up, we increase demand further by throwing even more taxpayer dollars at it. We do this in education as well.
Look at the price of health care before government spending on it, then look at it once the govenment spending started.