If you think something is impossible to do, you are bringing in necessity by saying that it necessarily can't be done.  Therefore, you can't do it and you will not try.  So the assumption that something is impossible may well trap you into making it impossible.  On the other hand, you may assume something is possible which is not, and just batter your head on a stone wall.

There's no unique criterion for coherence, but you have to be sensitive to incoherence.  And as we've said, the test for incoherence is whether you're getting the results you don't want.