In the book The Other Wes Moore, why does the author start chapter 6 off with Woody's graduation? What is the author's overall point?

I think the point of starting off the chapter—chapter 6, to be precise—with Woody's high school graduation is to highlight what can be achieved, even by those who've grown up in a similar environment to the other Wes Moore. Though the author Wes Moore doesn't ignore the many structural and societal factors that often keep back young African-American males, he nonetheless emphasizes the fact that choices can still be made, both good and bad. Woody has certainly made good choices; he's worked hard and, as a result, has been able to graduate from a school where less than 40% of students stay the course.
Starting the chapter in this way also allows the author to contrast Woody's experience with that of Wes. Unlike Woody, Wes didn't graduate from Northern High; he dropped out and pursued a life of crime. The consequences for Wes are disastrous. With a criminal record and no high school diploma, it's almost impossible for him to escape from his present condition and go on to make something of himself.