More often than not even the most structured, logical arguments based on obvious facts which are according to you impossible to refute, are not enough.
The emotional, political and personal elements cannot be ignored. This is the other half of the discussion which is so often under-estimated or even completely ignored.
Since humans are not machines nor are they 'really' logically-thinking beings, the good old ergo sum arguments are not very effective in the long term.
Each and every decision is by definition emotional. Even if the chances are a million to one and any efforts beyond say ten minutes seem to be futile, we the human beings believe so much in ourselves and the world around us, that we might even keep on going for a long time, despite obvious impossible-looking obstacles.
The funny thing is that quite often what at first seemed impossible becomes probable, and with a tad extra perseverance and positive thinking, happens before you realize it.
In that way life is pleasantly unpredictable and worth living, as always.