I was reading the following example from René Schilling's Brownian Motion. However, I cannot understand the final argument. Given that $X_t$ is a Brownian motion and $\mathscr{F}_t^X$ is its completed canonical filtration. Take $\mathscr{F}_t^{|X|}$ to be its analogue for the process $|X_t|$. Then why is it impossible to have $\mathscr{F}_t^X \subset \mathscr{F}_t^{|X|}$?
