There were storms around New York on Tuesday evening, and we sat on the runway for hours. I was heading to Dallas for Exxon Mobil’s annual meeting, which had become this year’s “can’t-miss” meeting, especially if you are a reporter.

Waiting for my plane to go wheels up, I pulled out The New York Review of Books; an article by the great physicist Freeman Dyson had caught my eye. It was a review of two books about global warming. Mr. Dyson argued that while there is clear scientific evidence showing that the concentration of carbon dioxide in the atmosphere has risen steadily, it does not necessarily mean that the end is nigh. Mr. Dyson talked soberly about the economic trade-offs involved in various solutions to cut carbon emissions, and agreed with the Yale economist William Nordhaus, author of one of the books under review, that some of the most radical solutions (especially some from Al Gore) would be “disastrously expensive,” and would damage the global economy.

Even more striking was his view that the science surrounding the havoc global warming would one day wreak on the planet was far from settled. He posed the real possibility that a low-cost solution would eventually manage the problem. He concluded that environmentalism had become “a worldwide secular religion … holding that we are stewards of the earth”— which for the most part was a good thing.

“Unfortunately,” Mr. Dyson added, “some members of the environmental movement have also adopted as an article of faith the belief that global warming is the greatest threat to the ecology of the planet. That is one reason why the arguments about global warming have become bitter and passionate. Much of the public has come to believe that anyone who is skeptical about the dangers of global warming is an enemy of the environment.”

So bitter and passionate, it turns out, that global warming can divide families. Even the Rockefellers.

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Last year was another fabulous year for Exxon Mobil. It made a record $40.6 billion in profits. It replaced its reserves, no easy task with oil so hard to find and extract these days. Its safety record was stellar. Its return on capital was an astounding 32 percent, another record. It spent $21 billion in capital investments while also paying out $36 billion on a combination of dividends and stock buy backs. It share price rose 22 percent.

You can argue, as many do, that this performance is nothing more than a case of holding out the umbrella while it rains money — that it’s all due to the dramatic run-up in the price of oil. But it’s a lot more than that. Exxon Mobil’s competitors are operating in the same environment, and they can’t touch its performance.

As he laid out the company’s results during a 45-minute speech that opened the annual meeting, Mr. Tillerson kept using the word “discipline.” “By maintaining discipline and rigor in everything we do” the company would continue to outperform the competition, he said, for instance. Discipline and rigor are indeed at the heart of the company’s engineering culture, and have a lot to do with why Exxon Mobil is so successful. When you’re spending literally billions of dollars building a refinery in China, as Exxon Mobil is, you can’t afford to be sloppy. “I wish our government were run as efficiently as Exxon Mobil,” said Fadel Gheit, an oil analyst with Oppenheimer & Company.

That discipline is drummed into Exxon Mobil executives very early — which gets at another characteristic of the company: it is extremely insular. Like most Exxon Mobil executives, Mr. Tillerson signed on in his early 20s and never left. And that bugs its critics. Many of those who spoke out against the company at the annual meeting — including Ms. Goodwin — talked about the need to bring “fresh perspectives” to the board. That, she said, was why she and other Rockefellers supported the resolution to bring in an independent board chairman.

“Their strength is that they are an inward-looking company with discipline,” said Mr. Monks, who has sponsored his independent chairman resolution for a half-dozen years. “Their weakness is that they are an inward-looking company with discipline.” He’s got a point; the same qualities that make Exxon Mobil the world’s best producer of oil and gas also cause it to be a terrible articulator of its own message. Its executives really only feel comfortable when they’re speaking to each other.

But let’s be honest here: gaining fresh perspective is hardly the primary reason the dissident Rockefellers got behind Mr. Monks’s resolution. The Monks proposal was a stalking horse for the issue that matters most to them: global warming. Most of the members of the family who are critical of Exxon Mobil are staunch environmentalists, who feel that “their” company should be doing more — much, much more — to help the world move to alternative sources of energy. Here they are on far shakier ground.

During his presentation to shareholders, Mr. Tillerson laid out Exxon Mobil’s core belief: despite climate change concerns, and efforts to come up with alternatives to oil, “there would be enormous growth in energy demand,” he said. And, he added, oil and gas would still supply over 60 percent of that demand in the year 2030. When it was her turn to speak, Ms. Goodwin passionately objected to that forecast.

Exxon Mobil’s projections “depend on two critical but untested assumptions,” she said, reading from notes. “First, developing countries will enjoy strong economic growth. And second, global consumption of oil and gas will significantly increase. This second assumption is wrong.” In her view, there was a high likelihood that new technologies would reduce the world’s reliance on oil and gas — and Exxon Mobil would suffer because of its stubborn refusal to spearhead new technologies back when it still had a chance.

What’s more, she added, if Exxon Mobil turned out to be right, and demand for oil and gas continued to grow for the next quarter century and beyond, that would bring about its own set of disastrous results — namely the environmental consequences of global warming. “It will cause weather disasters,” she predicted. “It will have a huge and harmful effect on the global economy upon which Exxon Mobil depends.”

What she and the other family members seem to really want is for Exxon Mobil to begin taking steps to transition away from the thing it does better than any entity in the world: find and produce oil. But where is it written that oil companies should be the ones to lead us into the promised land of alternative energy? The world doesn’t work that way. Transforming technologies will most likely come from innovators who have never set foot in an oil company, and don’t have an oil company’s baggage. Expecting Exxon Mobil to move the world to an oil-free future is a little like expecting buggy-whip manufacturers to invent the automobile.

What the Rockefellers were trying to do at the annual meeting is push Exxon Mobil toward their belief system — their global warming religion — and that is a place the company is unwilling to go. Its hard-headed view is that it is doing the most good for the most people by finding the oil and gas the world is going to need for the foreseeable future — and that global warming is not likely to lessen that need. Realistically, I find that notion difficult to disagree with.

As for Ms. Goodwin’s prediction of weather catastrophe, it could certainly happen. But it might not. We just don’t know enough yet. It would be lovely if we had new technologies that made the world much less reliant on oil but that’s not likely. India and China, just for starters, desperately need more energy to fuel their ambitions, and it is hardly fair to ask them to halt their economic progress — nor are they likely to do so. The best we can hope to do is dampen our need for oil — with such things as hybrid cars — by making, continual, small, practical breakthroughs. Believe it or not, Exxon Mobil has scientists working on precisely those kinds of practical breakthroughs.

In the end, most shareholders agreed with Exxon Mobil. And why not? If a company’s stock price is its report card, then Exxon Mobil is getting straight A. Ms. Goodwin’s primary resolution, calling for the company to produce a climate change report, got only 10.4 percent of the vote. Mr. Monks’s resolution got 39.5 percent — about the same as last year. The Rockefeller support made zero difference.

At his press conference afterward, Mr. Tillerson was asked about global warming. “My view is that climate change policy is so important to the world that to not have a debate on it is irresponsible. We don’t know everything about it. Nobody has this figured out. Anybody who tells you they have this all figured out is not telling you the truth. We have to understand that climate change policy, whatever it turns out to be, is going to hurt some people. But let’s at least have an open debate about it, so everybody knows what the facts are.”

Would that the Rockefellers had said something as sensible — and as disciplined — as that. Maybe next year.