The children of Aharon, Nadav and Avihu, enter the Mishkan in the Holy of Holies and offer an unauthorized sacrifice. For it they are punished with immediate death. In 10:3 Moshe says to Aharon, "That is what Hashem said By My close ones I shall be sanctified".
What a wicked person gets punished, people are understanding. They say he deserved it anyway. When a tzaddik gets punished it usually raises questions of faith. Why do bad things happen to good people, and the like.
These guys had heavy duty vitamin P (Protexia). There wer eonly 5 kohanim at the time, and they were two of them. They were the sons of Aharon. the nephews of Moshe. These are two people who are among an elite group and people hand-selected by God to lead the Jewish Nation.
With all that going for them, you would think they would be given a little leeway. Okay, so they did something wrong. We can let it slide. Nobody even knew they did anything wrong anyway - they did it in the Holy of Holies where nobody could see or know. Hashem could easily have slapped them on the wrist and said I will let it go this time just don't do it again.
But no. In My close ones I will be sanctified. When Hashem takes their lives, especially these people, as punishment for their actions, it makes the kiddush Hashem even greater. People see that the rules apply to everybody equally. There is no preferential treatment.
Moshe, Aharon, and families have to perform equally as, or even better than, everybody else. בקרבי אקדש.