how they could have lived

One of the reasons given for the death of the sons of Aharon was that they offered instruction in front of Moshe, their teacher. Again, this sounds scary. Almost all of us has had run-ins with our teachers. Does this mean that some angel will blow our brains out if we argue too much or too voiciferously? I mean, what is the limit , if any, for reasonable dissidence or personality clash?
I think this line of reasoning is misunderstood.
The real meaning behind it is, that a true Rav can direct the student properly .When the student defies the teacher he no longer can be taught the right way to do things. Beyond this, the Rav's
Holiness protects the Talmid's soul from deviating. Even after death , the Rav can remove the punishment from the student as Rabbi Yochanan says in tractate Chagigah 15b.
By defying their teacher , the sons of Aharon lost their protection from punishment, as well as the
defense that even if they erred now ,they will do better as per the inspiration of Moshe. Without Moshe's protective aura , they were left to the consequencs of their own actions.
Nadav and Avihu erred on several counts.
1) The Rav's opinion must be sought, if available-even when we don't agree intellectually
2) The Rav is not just a teacher ,he is the channel for the power of the Torah in this generation.
As such , listening to the Rav prevents errors .
3)The Rav embodies the Divine Attribute of Mercy and as such, his influence continues in the other world as well.
Rabbi Yochanan declared that he would take his students out of purgatory upon his death. Even a sinner as great as Elisha Ben Avuyeh was pardoned upon the passing of Rabbi Yochanan.
The Mishneh in The Ethics of the Fathers exhorts us to "make a Rav for yourself"! This is why
we Chassidim are so careful in our dealings with our Rav.