Edward speaks on this topic specifically to Bella in middle of the book:
"It's twilight," Edward murmured, looking at the western horizon. . . . His voice was thoughtful, as if his mind were somewhere far away. . . . "It's the safest time of day for us," he said, answering the unspoken question in my eyes. "The easiest time. But also the saddest, in a way . . . the end of another day, the return of the night. Darkness is so predictable, don't you think?" He smiled wistfully.
So, there you go, the safest time. In some ways, the most beautiful and the saddest time. Edward's answer is cryptic, however. My opinion burgeons from here into the idea that vampires can't be seen in sunlight, . . . and perhaps night is when their greatest lust for blood surfaces. Therefore, Edward is correct in his assessment.