a person says vaccines aren't necessary because they themselves are not vaccinated yet they're healthy; what fallacy is this?
user
That would be an example of argument from anecdote, where a particular instance is taken to be representative of the whole. This is usually an event experienced personally, or by a friend or family member, or a story which receives heavy media attention, and thus has a strong influence over the reasoning of the person in question.

We can see the utility of vaccines when we look at the aggregate statistics, and people who do not receive them will be at greater danger, but this does not mean that every unvaccinated individual will become unhealthy.
assistant
Without doing anything dangerous, how can I convince my mother to get her flu shot in the autumn?
user
I would recommend letting her know the statistics for how it can help her. Also another way to understand it can be finding another anecdote. The anecdote should be real and appeal to emotion but not to the level that would make them not believe that it won't happen to them. Then tell them that you love them and you don't want anything to happen to them.
assistant