I know that for a Chi squared test where we have $\Theta_0$ free parameters under the null hypothesis $H_0$ and $\Theta_1$ free parameters under the alternative hypothesis $H_1$, that $$2\log\Lambda \sim \chi_{\Theta_1 - \Theta_0}$$ It is also true that for $m>n$ that $\chi_m^{-1}(\alpha) > \chi_n^{-1}(\alpha)$. Thus, when $\Theta_0$ gets smaller (i.e. when we make our null hypothesis stronger) our rejection level $\chi_{\Theta_1 - \Theta_0}(\alpha)$ become larger.
My question is, why is this the case? I would have assumed that making our null hypothesis stronger would make it more likely that we reject it?