The two reasons given in the Medrash for the death of Nadav and Avihu are closely interrelated, each serving to explain the other. One Medrash states: “Nadav and Avihu died only because they had not taken wives.” The other Medrash states: “They (Nadav and Avihu )would go after Moshe and Aharon and ask: ‘When will these two old men die so that you and I can lead the generation?’” 

     It would seem that their failure to marry would not in itself have made them liable to death by the Hand of Hashem. Even as the Sages of the Talmud tell us that Ben Azzai chose to remain unmarried because "נפשו חשקה בתורה" - “his soul yearned for the Torah,” it could have been similarly assumed that Nadav and Avihu also had been so utterly devoted to the study of Torah that they did not want to assume the added responsibility of starting a family.

     However, the second statement clearly indicates that their failure to marry was not motivated by such noble ideals. For the position of leadership which Nadav and Avihu coveted would have left them little time for Torah study. Centuries later, the Tannaim would fast and pray so that they might be spared the responsibilities of communal leadership which would have taken them away from their sacred studies.

     Therefore, explains R’ Alexander Zusia Friedman zt”l (Mayana shel Torah) in the name of the Maharam of Vilna, if we know that Nadav and Avihu aspired to become leaders of the Jewish Nation, we know too, that their devotion to study could not have been all-absorbing to the extent that it would have explained their unwillingness to marry. The fact that they didn’t marry is considered a grave sin, unless it is motivated by a passion for the study of Torah. It was for this transgression that the sons of Aharon were sentenced to death by the Hand of Hashem.