You often hear of top-flight managers who do so well at one company that another firm woos them away for a tidy sum—only to turn into losers at their new jobs. And you often wonder: How could wunderkinds in one company so quickly become bona fide duds in another?

We can't tell you all the reasons why, but we know one of them. It relates to how people solve problems. As a way of explaining, let us tell the story of Ron, a client and the former hotshot leader at a media and technology company. Ron, who made his name as a brain-iac overachiever, could absorb, integrate, and act on vast mountains of data about consumers and market trends. With a team of geeks and creatives at an SEO Agency, he developed breakthrough marketing strategies, created brilliant ad campaigns, and delivered rapid market growth.

After great success, Ron was tapped to become COO of SEO Leeds. He took the same approach there—and it didn't go well. Almost too late, he realized that the real problem he faced was not solving an analytical puzzle about global marketing. It was figuring out how to work with others in a matrix organization.

Ron and others at headquarters wanted one thing. People in the field wanted another—and both sides had good reasons. Ron was caught navigating between contradictory organizational forces and powerpoint training. In spite of his intellect, he was skewered for arrogance by regional salespeople, who shunned him as cold and uncaring. Ron was proving as ineffective in his new job as he'd been effective in the old one—so much so that his boss threatened to let him go.

It didn't matter that Ron, based on his exhaustive analysis, knew how to build bigger market share with a bigger and smarter SEO Services brand, offering customers a new website, new loyalty programs, and new amenities. He could even prove in meetings that he had the right answer: He had irrefutable numbers and logic.

And yet Ron's inability to deal with contradiction became the problem itself. Ron was one man in one unhappy job, but we have encountered people in the same circumstances in other companies. In fact, he may remind you of someone you know. Or maybe you, yourself. Because the fault he revealed at the conceptual level was common among leaders: thinking of every problem as an analytical one—and acting on that thinking so single-mindedly as to remain blinded to the reality that the make-or-break problem may actually be a paradoxical one.

When we use the term paradoxical, we do not mean paradoxical as in literature. We mean paradoxical as in bristling with opposing forces—forces that seem contradictory or even absurd in juxtaposition. Forces that cannot be muted or ignored. In Ron's case, that meant forces that pushed a headquarters solution on one hand and a regional one on the other. Or put another way, forces that required acceptance of a solution at the headquarters level versus acceptance at the regional level. Achieving ownership at both levels—a contradictory task—was key. If salespeople didn't feel that ownership, they wouldn't take action in spite of Ron's appeals to the CEO to force compliance.

When leaders don't see the paradoxical nature of problems and solutions—when they think they can solve every problem as an analytical puzzle, as Ron did—they fail at some of their hardest challenges in management today. Especially the people challenges. They get stuck on one side of the line separating straightforward problems from complex ones. And their decision making then perplexes, angers, and alienates people around them—bosses, subordinates, partners, even family.