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 Now Nadab and Abihu, the sons of Aaron, each took his censer and put fire in it and laid incense on it and offered unauthorized fire before the LORD, which he had not commanded them.