What if someone said it isn't impossible, but there are big challenges, and based on your skill set, you're likely to fail. It is those kinds of non-glorified situations where perseverance is crucial, but it can also lead to spectacular failure.
I'd say, "Impossible != Unlikely"
based on your skill set, you're likely to fail
It's probably safe to say that almost everyone who ever achieved anything great was also "likely to fail". It comes with the territory.
it can also lead to spectacular failure
Spectacular failure is to great achievement what striking out is to hitting a home run.
...and that a more rational approach is to say, "The value of a possible success" is high enough that it's worth the expenditure of energy to bet the "losing" side of a p = .01 (or whatever)".
[of course it's going to depend on who is expending the energy - and who get what portions of the possible success benefits]