Its because people who would have died before having children now live, passing on the genetics. And realistically yes, becuase people live longer there are more and more treatments so the cost of your medical expenses for the span of your life is greater, and that expense gets spread through insurance and your taxes. As well, what you have to look at is the outliers in terms of costs are the most expensive. for instance, take a child diagnosed before birth through ultrasounds with Congenital Diaphragmatic Hernia.
http://fetus.ucsfmedicalcenter.org/cdh/learn_more.asp
Even just 30 or 40 years ago, guess what? that child would have been stillborn, or died within minutes to hours of being born. Now they have ways to diagnose it in the womb. It requires immediate surgery, plus potentially years worth of follow up surgeries. One of my wife's friends had a child with that. Spent her first year in the hospital in intensive care the whole time, and now at I think 4 years old hasn't gone more than 2 months without at least one major bad event of some sort that required a hospital visit, as well as having 5 or more doctors visits a month regularly. Her first year in the hospital was a mult-million dollar bill.
Ok sure, it doesn't raise the cost of your healthCARE but it does raise the cost of your healthINSURANCE as the insurance companies spread the cost over all the users. This is one of the bits of verbal sleight of hand that Obama used in getting obamacare passed, somehow trying to tie together the costs of insurance + care, which isn't truly accurate