American presidents don’t always get their way.

Most of them know that. Donald Trump, apparently, needed to be taught.

The dramatic decision by Mexican President Enrique Peña Nieto on Thursday to cancel a planned meeting with Trump wasn’t made for the benefit of Americans. Inside Mexico, where Trump is widely loathed, Peña Nieto faced intense pressure to back out of the summit. Trump continues to demand that Mexico pay for a wall at the border, as if he has the ability to simply boss around a sovereign democratic nation. By saying no — even at the risk of antagonizing the famously thin-skinned president — Mexico is making a stand for its own sovereignty.

But even if it wasn’t his intent, Peña Nieto is also doing a favor for the whole world, including many Americans, by puncturing the notion that Trump can simply get his way through the force of his bluster. It’s too bad Peña Nieto couldn’t deliver that message in person, but the important thing is that his message has been sent.

Building the wall was one of Trump’s key campaign promises. Now, even if a 2,000-mile wall through the desert were a good idea — and it’s not — at least it’s within the realm of the federal government’s power. The means of securing the nation’s border is a legitimate subject for the president and Congress to consider.

Whether a different country chooses to help is definitely not, which is why the second part of Trump’s campaign line — that he would force Mexico to pay for the wall — was the more dangerous part of that promise.

Trump seems to believe that, since he has demanded Mexico pay for the wall, anything less amounts to an insult to the United States. “Unless Mexico is going to treat the US fairly, with respect, such a meeting would be fruitless,’’ he whined after the summit’s cancellation. Respect, in Trump’s estimation, seems to mean that Mexico will do what he wants, when he wants it. Trump needs Mexico to knuckle under to protect the image he’s cultivated as a strong leader who gets his way.

But that’s not the way the world works. Ironically, Trump himself seemed to grasp that in his inaugural address, when he declared, “It is the right of all nations to put their own interests first.’’ Mexico’s interests, it turns out, do not involve spending $15 billion or more on a pointless wall just so Trump can boast of fulfilling a campaign promise.

Hopefully, Peña Nieto and Mexican residents realize that Trump does not represent all Americans, and that the ties between the two countries should be able to endure his presidency. But Trump’s demands of Mexico are putting that bilateral relationship, and the billions of dollars in economic ties it entails, in needless risk. Some Mexican officials have even floated the idea of pulling out of NAFTA.

Peña Nieto will probably face continued pressure from the White House to comply with Trump’s demands (although on Thursday there were signs that the administration was backing down, when Trump’s press secretary said that the wall would be funded with a 20 percent import tax). But whatever happens, the Mexican leader should hold firm — for the sake of Mexicans, who shouldn’t have to waste their money on a wall, but also of Americans, who shouldn’t have to live with a president who doesn’t understand the limitations of his office.