"Those who have false hope against the worst, never prepare for it."
"Prepare for the worst, hope for the best."
What does it mean to have false hope 'against' something? What is the difference between "hoping for" and having a "hope against"?
It is the difference between one claiming something is and is not possible. Typically one responds with 'hope against' to protect one's goals, ambitions - those controversial but not impossible. One responds with 'hope for' when they are protecting one's practicality - that they must consider more than mere idealism. These are social cues, not rigorous/propositional ones; except to the extent they say something about the speaker.
The major substantive behavior of 'hope against' is that hope is used as a means of dismissal of that which is 'hoped against'. When one is 'hoping for', there is a recognition of the fact it is hope, so long as it is taken literally. Figurative language will confuse most any distinction. 'Hope' is the operative word.
An example: "Hope against hope." One is hoping it is against the act of hoping that something will occur - hoping that it is more than possible: probable. This is not to indicate it is more probable than mere hope, but that they hope against it being merely possible that something will occur. In human behavioral terms, a human being 'against' something generally means the fight or flight response, since countenancing the subject 'hoped against' evokes anxiety. 'Hoping for' is the potential relief against what evokes anxiety, already countenanced.