Hypothesis testing seeks to reject a null hypothesis ($H_0$) on the basis of an assumption made about the sample following a certain distribution. This assumption is conditional on $H_0$ being true. So what is the flaw with the following reasoning?
If I reject $H_0$ in favor of the alternative hypothesis ($H_1$), I must then assume that (1) $H_1$ is true, and (2) that at the same time the variable under examination follows the distribution used to reject $H_0$. Since we also stated that the assumed distribution is conditional on $H_0$ being true, it appears that $H_0$ has got to be true in order to justify the assumption made about the distribution. Logically, it would therefore seem that both $H_0$ and $H_1$ have to be true, which is a paradox, because they are mutually exclusive!