Why do people not vaccinate their children?

There's a whole epidemic of chicken pox going on at nursery. This doesn't bother me a whole lot; both of mine have already had chicken pox. In fact, Luke had chicken pox when he was 9 weeks old, despite being exclusively breast fed so don't believe those stories that babies will get your antibodies through your breast milk. There is also a rumour of a few cases of measles here too. This doesn't bother me either; both of mine are fully vaccinated against everything.

The Bosnians also believe in vaccination, and have a schedule that is very similar to the British one; the only difference being that the children are also routinely immunised against TB whereas in the UK they inoculate those children they think are more at risk.

Which is why I was so surprised to have a conversation with a parent here that went along the lines of this:

Parent: I'm very worried about the outbreak of measles.
Me: Oh, measles isn't good but if your child has had the vaccine then there should be nothing to worry about.
Parent: We don't believe in vaccinations. Our child hasn't had any.

Now, I'm a fan of parental choice. I think that everyone should be able to choose how they want to bring up their children. There is only one parental decision that I have any strong opinion on, and that is that every single child should be vaccinated. These childhood diseases can be killers. They are serious and they can be controlled but to do so everyone needs to inoculate their children.

I'm not really talking about the MMR here (MMR being the combined vaccination for Mumps, Measles and Rubella which was linked to autism in children in the late 1990s, the research of which was later discredited). After all, you can still vaccinate your children separately against these illnesses if you don't want to have the combined vaccine. No I'm talking about those who choose not to immunise their children at all. I simply don't understand this decision.

Is it because most people do immunise their children reducing the likelihood of an epidemic, meaning that some feel they can afford to run the risk of not inoculating their own? But, at the risk of offending a few people, isn't this quite a selfish form of action to take? Everyone else can have the inoculations so we don't have to?

Is it because fit and healthy children can usually throw off these illnesses without long term damage? But some children are not fit and healthy, some are not able to be vaccinated. By allowing the potential of a spread of disease, surely these more susceptible children are being exposed unnecessarily?

Back to the conversation. I spluttered a bit before finally muttering something along the lines of being very pleased that mine were fully vaccinated and headed off. British you see - don't like unnecessary conflict. But the conversation has been playing on my mind for a few weeks now. So I thought I'd bring it out in the open here and see if there is anyone out there who can shed light on why they believe that no vaccinations is a sensible choice. Am I the only one who struggles to see the sense in this course of action?