Based on the chiddush of R' Chaim Soloveitchik we can better explain the significance of the ikakrim. The problem with the Rambam's list (as noted by the Sefer haIkkarim) is that if it means to include only fundamental principles, it is too broad; if it means to include all necessary beliefs, it is far too narrow -- not everything a Jew is required to believe is included in the ikkarim. So what makes these 13 special?
R' Chaim held that the ikkarim must be affirmatively believed. It is not the sin of denial which makes one into an apikores (in which case context and cause would be valid considerations), but it is the lack of positive affirmation, which no excuse can substitute for, which seperates believer from heretic. Even if one does not affirm the ikkarim because of a misunderstanding or lack of knowledge, that failure practically sets one apart from the Jewish people. Other beliefs may be no less fundamental, but it is only the sin of intentional denial which would violate the prohibition against minus.