The government is trying to get this through by saying that all women need and deserve this service. Yet they don't demand sun block for an even bigger problem.
Quinn, perhaps I can offer some insight into why some people consider contraception to be a much bigger consideration than simply having sex or not, and why some people would think that your analogy to sunblock would not be relevant.
There is a strong current of American thought that believes that freedom is not merely the total of abstract legal principles, and that the legal protection of property and conscience is simply not enough to secure individual freedom. There were many that came to America, who had either or both legal property protections or were comfortable with their level of freedom of conscience. However, despite having abstract rights to own property (serfdom was dead in much of Europe by 1776, and was gone from all of Europe before we abolished slavery.) European property (especially land) was locked into the hands of a few because of yes- strong legal protections of property. There was no practical way for the poor to get access property. They had the right to, but no reasonable path.
This issue is critical in understanding some peoples' notions of freedom. Property is not merely the measure of your hard work, it can be seen as the basis of any actual "real legal and political freedoms." If you have no property from which to support yourself, you will soon sell many of your legal and political freedoms in order to eat. If you are dependent on a landlord, or factory owner, or corporation for existence- it is very difficult to exercise any other forms of independence from their points of view. etc.. Freedom is only possible with independence, independence is only possible with a certain level of property. The property itself rather than property rights can be seen as the basis of freedom.
Examples- The Regulator movement, Declaration of Independence complaining about the Proclamation of 1763, Free Soil Party, Lincoln's Republican Party: Thaddeus Steven's said that legal protections of ex slaves was not enough, freedom required property- 40 Acres and a Mule etc
–“If we do not furnish them with homesteads and hedge them around with protective laws ; if we leave them to the legislation of their late masters, we had better have left them in bondage.”
In other words, many people argue that property rights only work for people who have acquired enough property to be independent of others, and that strictly constructed property rights often have the unfortunate effect of locking some into dependence, even if they are also theoretically free to own property themselves.
Where this comes to contraception is that many people in the 2oth century began to argue that women were "enslaved to men" not merely because of legal restrictions, or biblical/cultural norms, but that the economics/biology of the gender situation were constructed in a way that fostered it, and that public policy could help correct it. They felt if government could be used to reinforce biblical patriarchy and economic patriarchy, it could be used to alleviate it, reverse it and overcome it as well.
These women's rights (Margaret Sanger and many others) advocates argued the thing that most restricted women's freedom was lack of access to biological knowledge and common contraceptive technology. In other words for women to be truly independent of men they needed economic independence from men, and the stumbling block was poorly timed pregnancy. If you are not materially independent, a pregnancy is going to put you into a state of dependence- often on men: your father, your husband, your boyfriend, the dole- someone will have to support you and in the process you lose your freedom.
So, for some the concept of women's reproductive health is not merely about disease, or ensuring a good time on weekends. To some it is the only pathway for women to ever have "freedom" and independence in society. That is why sunblock is not going to be seen as an effective analogy to some. They argue that access to reproductive knowledge and education, and access to affordable contraceptive technology is the only pathway for freedom. Sunblock, though a legitimate health issue, has much less bearing on the reality of freedom, property, and independence.
I am not sure you will accept any of their argument, but it may explain why some people are so very adamant about reproductive health issues for women- they see it as the only foundation for real freedom and independence from patriarchy.