Everybody has a right not to vaccinate him- or herself. Government-enforced vaccinations have quite a few problems. They all stem from the fact that weighing the positives and negatives of getting vaccinated is a personal choice, one which the government should not make for you.
Plenty of people don't like needles. I'm one of them. I've evaluated the statistics on the H1N1 flu and concluded it is not worth the anxiety of getting vaccinated to avoid a negligible chance of serious illness. Who is the government to say otherwise? But this isn't just a libertarian argument; there's also a practical aspect to this. Either we consider it reasonable to subject people to anxiety-inducing situations (the stress of which can be rather extreme) against their will, or we have to allow for people to appeal to opt out. I find the former possibility to be barbaric.
The latter possibly requires some sort of authority to evaluate the appeals, and this is a nontrivial logistical concern, a waste of money for sure. Worse than being financially irresponsible, such an authority would have to develop criteria that probably would not fit everybody. How can a state authority be expected to weigh the relevant variables (your anxiety versus the health concerns) more accurately than you yourself can? Would you need a diagnosis of an anxiety disorder to qualify to opt out? (I personally find the psychiatric disorder model and the concept of psychiatric disorder to both be highly bogus, but that is not the topic of this thread, and whether the diagnoses represent relevant medical details is tangential to the fact that they are the type of thing such an authority would consider.) Would you need some past history of incidents at vaccination sites? If just your word is good enough, then the same people who don't get a vaccination now (for any reason) would just opt out. As far as I can tell, the only practical way to implement mandatory vaccination would be to make it mandatory for everybody, even the people for whom it causes major anxiety issues, and this is unacceptable.
In addition to anxiety concerns, other negatives might include scepticism about the efficacy of the vaccine. The government is not properly positioned to evaluate these concerns for everybody. It is a personal choice, one that affects the integrity of your own body. You should have the right to control what goes into your body.
Moving past your personal rights, what is even the state's interest in restricting your freedom in this particular instance? The only relevant argument I can imagine applies if the state is subsidising the health care of people afflicted with the disease. I'll divert the question of whether the state should do this at all to some other discussion and note here only that the solution to this is simple: people who choose not to vaccinate themselves should have to pay the full cost of their care.