R. Shlomo Kluger answers:
It is written in Koheles (8,8) “there is no ruling on the day of death”, and Chazal explain that for this reason David is not referred to as ‘King David’ when discussing his death, because on the day of death one is not a ruler. And since Chazal explained on the verse in Bamidbar (18,8) “Behold, I have given to you all the holy things of the children of Yisrael for distinction” - for greatness, like the kings eat, it is clear that the priesthood is considered like royalty, and thus the verse “there is no ruling on the day of death” applies to them also.
Therefore, since on this day two of the sons of Aharon died - and in truth all of them were liable to be killed as the Midrash on this parsha teaches - for them this was a day of death, and so they were not referred to by their title of authority. And it is for this reason that the Torah commenced the parsha by saying “ויהי (an expression which Chazal taught indicates that a distressing event happened at that time) on the eighth day” in order to hint that it would be a day on which there was to be a distressing event, and therefore it was not fitting to refer to them as Kohanim in this parsha because there is no ruling on the day of death.
Full text in English can be found here.