Unassailable means that something cannot be attacked successfully — nobody can knock it down, weaken it, or take it away. The picture underneath is a castle wall that no army can break, and English keeps that picture in three everyday uses. First, arguments and evidence: an unassailable case is one with no weak point for an opponent to hit. Second, reputations and positions: an unassailable reputation is one that gossip cannot damage; an unassailable leader cannot be pushed out. Third — and this is where Taiwanese students meet it most — sport and competition: "an unassailable lead" is a lead so large that the other team can no longer catch up, no matter what happens in the time left. Sports commentators use this constantly, and it is the most concrete way to feel the word. It is formal and a bit grand; you would not use it about small things. Note the honest hedge in it: unassailable is a judgement about the present, and history is full of unassailable leaders who fell the next year. Good writers know this, which is why the word sometimes appears with a hint of irony.