This needs a lot of revision:
Many people often assume their assumptions are correct.
Um, this isn't strictly speaking a truism, but it comes close enough that you probably don't need to state it.
They do not deem the correct answer to be necessary, instead, they rely on their own logic to choose the truth - and in doing so, they allow a margin of error.
There are multiple things wrong with this sentence. First, it is a run-on. Second, the correct answer to what? In what sort of situations? You need more context, as this doesn't really work as a generalization. Third, what do you mean by "own logic?" In what ways can there be multiple logics? Fourth, can you choose the truth in the sense you mean? If they do choose the truth, then wouldn't they be right, in fact? Fifth, if they allow for a margin of error, then your first sentence is completely wrong.
It is my hope that one day, this changes.
Given how little sense your first paragraph makes, the "this" here is wholly unclear.
That Presidents will analyse all information before launching wars
What makes you think they don't?
hat Generals will review their battleplans before sending men and women to die,
This they certainly do.
Teachers will question their own decisions before handing out punishments.
At least some must.
That Everyone, will stop to question their own motives and think for a moment - 'Could I be wrong?'
This isn't bad advice, but you haven't shown that this isn't already prevalent, or said anything particularly thoughtful beyond this.