There are whole books dedicated to it (I can recommend Bernouilli's Fallacy by Clayton), but the gist is: NHST answers the wrong question (it should answer: what is the likelihood of the hypothesis given the data, but answers: what is the likelihood of the data under the hypothesis), and is (thus) very sensitive to the probability of the prior. To quote the old example: when you wake up with a headache, it's not usual to assume you've got a brain tumor.
There are whole books dedicated to it (I can recommend Bernouilli's Fallacy by Clayton), but the gist is: NHST answers the wrong question (it should answer: what is the likelihood of the hypothesis given the data, but answers: what is the likelihood of the data under the hypothesis), and is (thus) very sensitive to the probability of the prior. To quote the old example: when you wake up with a headache, it's not usual to assume you've got a brain tumor.