"It is not the case that e necessarily implies d", would be the formalized English representation of that logical statement. Implication, within the Logical Calculus, is a fact. "does not necessarily imply" means, formally, "does not imply". That's the he problem with translating formal language to natural language and back again.~( e -> d ).
Being right, does not endow the right to be rude; politeness costs nothing.
Being unknowing, is not the same as being stupid.
Expressing a contrary opinion, whether to the individual or the group, is more often a sign of deeper thought than of cantankerous belligerence.
Do not mistake your goals as the only goals; your opinion as the only opinion; your confidence as correctness. Saying you know better is not the same as explaining you know better.