Under Armour CEO Kevin Plank's full-throated praise of Donald Trump as a can-do, business-friendly president during an interview on CNBC this week prompted a quick backlash on social media — including some unflattering comparisons to Nike CEO Mark Parker, who late last month sent an email to his employees opposing the president's travel ban from seven Muslim-majority nations, saying the company “stands together against bigotry and any form of discrimination.” The backlash has now prompted its own backlash, with Trump supporters tweeting out promises to order Under Armour gear for the first time.

Time will tell whether aligning Under Armour with a deeply polarizing and increasingly unpopular president is a good business strategy (though it is worth noting that the company's biggest star endorser of the moment, New England Patriots quarterback Tom Brady, a personal friend of Mr. Trump who was once spotted with a Make America Great Again hat in his locker, has been dodging questions about the president for months). Even if Mr. Trump weren't a controversial figure, it would be curious that the CEO of a company that relies on a global supply chain and sees its biggest opportunities for growth in international markets would cozy up to a rabid opponent of free trade.

On Wednesday, the company put out a statement saying it engages in “policy not politics” and emphasizing the value Under Armour places on diversity and on “fair trade, an inclusive immigration policy that welcomes the best and the brightest and those seeking opportunity in the great tradition of our country, and tax reform that drives hiring to help create new jobs globally, across America and in Baltimore.”

But what is clear is that Mr. Plank's comments highlight the fallacy of the notion that being successful in business is an inherent qualification for success in government.

“I think he's highly passionate,” Mr. Plank said during a Tuesday interview on CNBC's “Fast Money Halftime Report.” “To have such a pro-business president is something that is a real asset for the country. People can really grab that opportunity. He loves to build, I don't think there's any surprises here. When you look at the president, he wants to build things. He wants to build things he wants to make bold decisions and be really decisive. I'm a big fan of people that operate in the world of publish and iterate versus think, think, think, think, think. So there's a lot that I respect there.”

Mr. Plank, himself a bold, risk-taking, move-fast-and-break-things builder of a rapidly growing company, evidently can identify with the new president. But he and others who idealize the notion of the president as America's CEO fail to understand the radically different responsibilities and stakes of the two roles. If Mr. Plank decides to “publish and iterate,” he maybe puts out some running tights that chafe or Stephen Curry shoes that get mocked as best suited for the early bird special at the nearest buffet. If Mr. Trump does, a 5-year-old boy gets separated from his mom and detained at Dulles for several hours. Mr. Trump wants to “publish and iterate” when it comes to the rapid repeal of the Affordable Care Act without a viable replacement in hand, but even Republicans in Congress are shying away from a course that could lead to 32 million people losing insurance in the first year and an annual increase in deaths of perhaps 24,000. Mr. Plank is responsible for Under Armour's stock price. Mr. Trump is responsible for the nuclear codes.

Yes, President Trump wants to build things. So did President Barack Obama (albeit not CIA black sites or a giant and almost certainly ineffective wall on the Mexican border). But unlike a corporate CEO who also happens to be the largest shareholder in the company he runs, presidents can't build anything without support from Congress. Granted, the Republican-led House and Senate appear willing to blithely reverse themselves on any issue to suit President Trump, but it is worth noting that his idea for pumping money into rebuilding roads, bridges and the like, and the mechanism he has suggested to pay for it, were blocked at every turn when Mr. Obama suggested nearly the same thing. Perhaps Mr. Plank would have a greater appreciation for President Obama if the majority of Under Armour's board was appointed by Nike and made it their mission to oust him, even if it required destroying the company in the process.

Finally, Mr. Plank might want temper his admiration of a businessman-president by considering this. If President Trump pumps out tweets claiming that he had the largest ever inaugural crowd or that he only lost the popular vote because millions of people voted illegally, despite evidence to the contrary, his administration brands them “alternative facts” and blames the media for obsessing about them. If Mr. Plank falsely tweeted that his company had its best sales quarter ever, that would be called securities fraud, and he would risk going to jail.

If Mr. Plank's customers are unhappy with how he's running the company, they can stop buying his products. If his shareholders are dissatisfied, they can sell Under Armour stock. (Quite a few have of late, though not because of Mr. Plank's views on the president.) By contrast, 320 million people must now rely on President Trump to safeguard their life and liberty whether they like it or not. It might not hurt for him to think, think, think, think, think.