Laman made a request, and it was denied. There is no explanation for why Laban was angry enough that he threatened to kill Laman, other than the accusation that Laman was a robber.
Of course, Laman had made no attempt at robbery, and this was a false accusation. It is possible that Nephi made sure to enter this exchange to give his readers a picture of Laban’s character. By the time Nephi wrote, Nephi’s slaying of Laban was decades in the past. Showing Laban as an unprincipled man, who would accuse Laman of robbery when there was only a request, gives the reader a picture of an unrighteous leader. By the time we reach Laban’s end at Nephi’s hands, we (as readers) will not be sorry to see him go.
The aftermath of this event is important. Jehovah himself had chosen Laman to go to Laban. Laman had failed. If Jehovah’s choice had failed, it must have been seen as an impossible task. It was certainly seen as a dangerous task, because Laban had threatened Laman’s life.
The heavy melancholy of failure hovered over the brothers, and the desire was to accept defeat and return to their father.