It’s interesting how this OP phenomenologically reduced (literally) the concepts of faith(good or bad), free will, rationality/faith (as in either/or), being, nothingness, etc. The necessity of annihilation comes not from free will, as though it was a moral imperative, but as grounded in counter logic. If you were to say that Being and Nothingness have a logical relationship, then the next step to take is to say, we could not make the distinction, if it were not for the fact, that we have to introduce a third element, (nihilism), to be able to make the distinction. It is of logical necessity to nihilise, in order to distinguish one from the other. But the distinctions are then, reduced to a nominal -definitional distinction. If the logical reduction is not made, the idea of annihilation itself, is not possible. Therefore the reduction is prior.
In fact there is no logical need to reduce, only if you intend to make the distinction. (Between Being and Nothing-ness). So intentionality, as I understand it become the key. To the whole process. But why?
What is the object of the intention? Or it’s ground? Well that is a tough one, but another differentiation comes to mind between continental philosophy and empirical/utilitarian philosophy. The motive behind continental philosophy is traditional, and has its genesis in mostly german idealism, and existentialism grew quickly as a method to quickly align with the political crisis that was emerging c. 1848-1945. The urgency and desire to reduce the phenomenological basically cartisian-heglelian duality, -into marxian terms (sartre)—was the motivation. The ground was the economic (marxian interpretation of hegel)
So, faith in nihilism, is like looking glass. What can be seen there? A preoccupation with moral imperatives? In order to avert the dramatic revolutionary conflicts? Or is there more? A severe pessimism of political motives ascribing some connection with the notion that civilization’s discontents were basically due to repression on extremely basic levels? What can be seen? Delusions of mythic proportions on wagnerian scales again to compensate for a reality bankrupted on fallen idols?
Probably all of the above. That it didn’t work is obvious. Revolutions for idyll, bachanalles and such always reminders of who cleans up after the party, and somehow no one wants to, because everybody thought that the party would last.