Israel refrains from military parades not because "in its self-conception is the losing side (or worse: the sinner)" but because we want to project others and to inculcate in our children non-militaristic values. We value military service and bravery and heroism and self-sacrifice, but the first goal of our military might is to prevent wars. Winning them is the second choice.
Israeli soldier lightly wounded after being hit by car south of Hebron (Haaretz)
from the article: It is time to free ourselves of the false 'fiasco’ of the 1973 war