2SAT Problem using Implication Graph
For any variable $X$, if there is a path from $X$ to $\neg X$ then you cannot set $X$ to $True$, since otherwise you would end up with a $True \Rightarrow False$ implication somewhere along the path. For the same reason, if there is a path from $\neg X$ to $X$ you cannot set $X$ to $False$. 

Hence, in the first case you must set $X$ to $False$, in the second you must set it to $True$. If there are paths in both directions, as you already know, the formula is not satisfiable. 

In your example, there are only paths from $X$ to $\neg X$ for all variables, hence the only assignment that satisfies the instance is the one where all variables are $False$.