The difficulty bar is just an approximation based on a "normal" player's skill and the strength of your bears. It is possible in some cases to win even when the difficulty says "Impossible" if it was just barely impossible and if the player does much, much better than expected. So if you have nothing else to use your honey on, go ahead and give those "Unprepared" or "Almost Ready" matches a try if you haven't already.
In Story Mode, a very good player will have a lot of "Unprepared" or "Almost Ready" matches because he/she has been "punching above his weight" and has already beaten missions that a "normal" player hasn't yet beaten.
Some of the other game modes (Daily Events, School, and non-tournament Special Events) have dynamic score-setting based on the game's perception of the player's skill. This makes the score target higher or lower so that we can use the same board for everyone without the strong players getting bored or weak players getting frustrated. If the game currently thinks that you're quite skilled, it will set the target higher accordingly. You should try anyway--if you win, you'll win! And if you lose, this will help the game to tweak the skill perception (and thus the target scores) down over a number of days when it sees that you're not doing so well.
- Note that we don't use dynamic scoring in Story Mode, except for very early in the story to make the early missions a little less trivial for good players. If you're stuck in Story Mode, that's probably on you and your bears, not because of dynamic scoring. This page has some tips for folks who are stuck in Story Mode.