The first time I saw Barack Obama in the flesh was at Kingstree High School in South Carolina. It was January 2008, early in the presidential campaign, when people were still not quite sure what to make of the "skinny guy with the funny name," as he called himself.

The crowd there were mainly African-American, which marked a change after the almost all-white audiences of Iowa and New Hampshire. It also represented Obama's first chance to reassure hitherto-sceptical black Americans that he was, indeed, one of their own.

In his manner, in his speaking style, he demonstrated just that – and swiftly. "I need you not only to vote, but I need you to get cousin Pookie to vote," he said, with a smile. "I need Ray-Ray to vote." Anyone who ever doubted whether Obama was "black enough" left Kingstree that morning with no such doubts.

But the candidate did not just tickle his audience's tummy. He told them some uncomfortable truths too. He told black fathers they needed to stay with their children, that parents needed to help their kids with their schoolwork, that black America needed to offer role models besides rappers and athletes.

I've been thinking of that morning in Kingstree after reading the speech Obama gave last night to the National Association for the Advancement of Colored People, America's premier civil rights organisation. It was yet another stirring address – though we're getting used to those. But it also adopted the shape that now seems to characterise some of Obama's most effective speeches and which was on display, if only in outline, all those months ago in South Carolina.

First, the president stresses his solidarity with and affinity for his audience. To the NAACP, that came through a powerful attack on America's long history of racism and his admission that that is far from being in the past: "the pain of discrimination is still felt in America," he said. That empathy came with a lot of practical talk on remedies, in employment, education and healthcare.

Once solidarity is established, Obama then feels able to tell some home truths. Yesterday that echoed Kingstree very directly:

To parents, we can't tell our kids to do well in school and fail to support them when they get home. For our kids to excel, we must accept our own responsibilities. That means putting away the Xbox and putting our kids to bed at a reasonable hour. It means attending those parent-teacher conferences, reading to our kids, and helping them with their homework.

And this:

They might think they've got a pretty good jump shot or a pretty good flow, but our kids can't all aspire to be the next LeBron or Lil Wayne. I want them aspiring to be scientists and engineers, doctors and teachers, not just ballers and rappers.

Imagine a white president saying these things. He either wouldn't dare or, if he did, it would sound like finger-wagging and hectoring, whose motives would always be suspect. People might well accuse such a president of racist bias, playing on a stereotype of black youth as "ballers and rappers".

But Obama does not face that obstacle. He is addressing black America from within. He can speak of "our children" and "our communities" and mean it. And people are prepared to take criticism from within – from one of their own – that they would never tolerate from an outsider.

Obama used that fact to his advantage when addressing African leaders earlier this month. "I have the blood of Africa within me," he told them – before launching a stern lecture on corruption and civil war, adding that Africans could not blame their former imperial masters for all their woes. Yesterday he offered the NAACP a variation of the same theme:

Your destiny is in your hands, and don't you forget that. That's what we have to teach all of our children! No excuses! No excuses!

He even used that approach in his landmark speech to the Muslim world last month: My middle name is Hussein, I have Muslims in my family, I have reverence for the Islamic faith – but here's where you are going wrong.

It is this ability, to speak to a range of constituencies his predecessors would have found out of reach – and to speak to those constituencies from within – that sets Obama apart. And which means his presidency still retains the chance to be transformational.