Those who idolize former President Barack Obama believe he is everything President Trump is not.

He has a thoughtful manner and was not just professorial in lecturing the public, but was indeed a former professor. Even Trump's most fervent supporters would not suggest their man has a professorial and learned demeanor. Indeed, he is liked in part because he lacks those qualities, coming across as ready to brush aside those academic niceties and get down to action.

Obama also famously disdains drama — one of his nicknames was "No Drama Obama" — whereas his successor seems to thrive on it. Comedians found Obama difficult to mock, but late-night comedy can't get enough of Trump. (This says as much about celebrity politics, of course. Celebrities flocked to Obama, and even pledged allegiance to him, yet now pride themselves on being part of the self-aggrandized #Resistance to Trump.)

In short, Obama was cool. Trump is not.

This difference has, however, led to a big mistake in assessing Obama. Because of his cool, his professorial demeanor, and his thoughtful air, supporters ascribe to Obama an enduring streak of propriety. They think him innocent of arrogance and self-regard, qualities for which they detest Trump.

But Obama's demeanor is a camouflage for an ego and a demand for attention every bit as overweening as Trump's. Throughout his presidency and since, Obama displayed his own gaucherie. An early example was in 2009 when Democrats feared they faced another 1994-style wave election — they did indeed — because of the deeply unpopular healthcare law they were foisting on the country. "Well," said Obama smugly, apparently to calm their nerves, "the big difference here and in '94 [is], you've got me." His presence, he claimed, would stop the rising tide of Republican support. Trump could not have said anything more arrogant. And, as history recalls, Obama couldn't stop the tide of GOP votes any more than he could fulfill his messianic claim of stopping sea levels from rising.

But there are far more recent examples of Obama's massive self-regard, and his belief that decorum and tradition don't apply to him. Last week, he essentially trolled Trump during the president's first official trip abroad. When Trump was with NATO leaders in Brussels, Obama made his own visit to Germany, there to be feted by Chancellor Angela Merkel. His invitation to this event to celebrate the 500th anniversary of the Protestant Reformation had been delivered a year earlier, but he accepted the invitation only a month ago, in full knowledge that he would be coinciding with Trump's own visit with Merkel, which could be expected to be less cordial. It is impossible to believe anything other than that Obama accepted with the express purpose of creating a contrast that would put Trump at a disadvantage. This is not what a genuinely decorous former president does.

To no one's surprise, Obama's choice to make this trip encouraged comparisons by the news media, whose darling he is. They gleefully portrayed him as upstaging a sitting president. As if to make plain his animus toward his successor, Obama took swipes at Trump, saying, for example, Americans "can't hide behind a wall" in order to isolate themselves from the world's problems.

Obama helped Merkel, who is in the midst of an election campaign, as she suggested to an anti-American German electorate that the country and Europe could no longer rely on the United States. (It should be remembered, however, that she said much the same thing when Obama was president, so the truth, if not her intentions, are doubtful). But she decided that it would help her to campaign against Trump, and Obama lent her a hand. It was at a campaign rally, after all, that she said, "we Europeans must really take our destiny into our own hands."

Trump's approach to Europe is controversial. He has taken a hard line with allies in pressing them to pay their agreed share of NATO costs. Obama has the same legal right as any American to criticize his president, but as a former president he has a higher responsibility to let his successor govern, and to help him succeed if he can. He should certainly not be preening and burnishing his reputation using the current president as his foil. It is a cheap, unbecoming and tawdry way to behave.

President George W. Bush waited years before commenting on Obama's presidency, explaining in 2009 that his successor "deserves my silence." And when he did break that silence, Bush didn't do it while parading with foreign leaders.

Professor Obama sometimes referred to events as "teaching moments." This is another one. It is to be hoped that he learns to get off the stage — he's had his time — and to maintain a more dignified silence.