We may speculate about their motives.
They were impressed by their newly acquired dignity as priests.
They were in an elevated mood as they had gone through a seven-day consecration. They wanted to prove and distinguish themselves.
Their father was not a strong character and they were young.
They were proud and ambitious.
They were eager to show off their newly acquired dignity as priests.
The present solemn ceremony with a large crowd of people present, all of them impressed by what was going on, may have prompted them to feel: this is the right moment!
1 Les fils d'Aaron, Nadab et Abihu, prirent chacun un brasier, y mirent du feu, et posèrent du parfum dessus; ils apportèrent devant l'Eternel du feu étranger, ce qu'il ne leur avait point ordonné.