(I am not sure this answers the question 'Why?', but hopefully it normalizes the feeling and gives it some context.)
This happens, grammatically, because necessity and sufficiency are a complementary pair of modes.
Modal verbs have natural complements. Should, and May (in the most proper sense, not the sense of ambiguity.) are complementary: What one is not obligated not to do is something one is allowed to do. In a short form dodging the risk implicit in English negations: not(should(not X)) = may X.
So are Can and Will (again in the most proper sense): What one is not capable of not doing is something one is predictably always going to do. Parallel to the above, not(can(not X)) == will X.
In this case, not(must(not X)) = might X. Sufficient conditions can always be put in the form "whenever X happens Y must happen". And necessary conditions can always be put in the form "only when X happens might Y happen." So from the sufficient condition "whenever X does not happen, Y must not happen" we can deduce the necessary condition "only when X happens, might Y happen".
These are complementary (or dual), not opposite; because in this case the two negations do not get you back to the original statement. You end up, instead, in the complementary stance. The traditional notation for this is ¬¬p = <>p, (as distinct from ¬p = <>p, which is false). Here the box represents the more restrictive of two complementary modes and the diamond the more constructive one.
Unfortunately, sticking with this basis in the language is difficult because our use of modality slides around all the time. In particular, the phrasing of necessary conditions varies because "can" and "may" are often used to express "might", and vice versus. We simply are not consistent enough to be specific. (The Germans lent us nice things to play with, and look what we have done with them.)