Momochi Zabuza had felt well enough to attack that night despite the customer's orders which had something to do with some dramatic posturing on that incomplete bridge. As a missing-nin, he was free to say that the customer wasn't always right.
It had been almost completely by chance that he had encountered Sharingan no Kakashi before anyone else. When he said almost, it was because there had been certain sounds that had alerted him to the man's presence.
Haku - who had been reluctant to kill - had been almost eager in this instance.
While such things as what had been going on between Kakashi and his student whom Haku was inordinately fond of did happen, and people actually paid for such things to happen sometimes, there was a difference when it was a relationship such as this one.
The relationship between a Jounin who was assigned to teach and his Genin students was held sacrosanct throughout all of the countries on the continent. It had to be, considering how easily an instructor could damage the young ninja who were the village's future without even trying. A shinobi acting out of maliciousness and spite could doom a village, and not just by churning out a number of substandard ninja with more issues than a long-running weekly publication. Normal instructors did that often enough.
Violating one's vows as a Genin instructor in this manner was a far worse a crime than its counterpart in the Civillian sector - the relationship between an elementary/junior high/ or high school teacher and his/her student - if only for it's potential fallout, since Civillians didn't tend to blow up several neighborhoods when they finally lost it.
People would be lining up to kill this guy. Unfortunately for them, it was a first-come-first-serve situation, and he and Haku had gotten there first.