With $x_2 + x_3 \le 2x_4$, you see that $x_4$ can be $0$ or $1$ only if both $x_2$ and $x_3$ are $0$. In any other case, $x_4=1$. If you want to enforce a constraint that "$x_4=1$ only if $x_2$ and $x_3$ are both $1$", then you can have $x_4 \ge x_2 + x_3 -1$.

With $x_2 + x_3 \le 2x_4$, you see that $x_4$ can be $0$ or $1$ only if both $x_2$ and $x_3$ are $0$. In any other case, $x_4=1$. If you want to enforce a constraint that "$x_4=1$ if $x_2$ and $x_3$ are both $1$", then you can have $x_4 \ge x_2 + x_3 -1$.