A great politician isn’t necessarily a presidential one. This week, Americans saw one of their greatest politicians frankly sharing his doubts about running for the highest office and another drop out of the race.

In an emotional interview with The Late Show‘s Stephen Colbert on Thursday, Vice President Joe Biden reminisced about speaking to military families shortly after losing his son, Beau, to brain cancer in May when a soldier stood up and announced himself as having served with the younger Biden in Iraq.

“I lost it,” Biden said. “You can’t do that.”

“I don’t think any man or woman should run for president,” he continued, “unless they can look at folks out there and say, ‘I promise you have my whole heart, my whole soul, my energy and my passion.’ I’d be lying if I said that I knew I was there.”

It’s no wonder Biden is one of America’s most beloved politicians. It seems no one can speak frankly like him — if sometimes to the embarrassment of himself and others — and survive in national politics.

The Democrat spoke about that as well, wondering, “why in God’s name would you want the job if you couldn’t say what you believed?”

But a leader shouldn’t always say what’s on his mind. It’s not just that the media and voters can be unforgiving when a politician slips — although Biden seems uniquely immune to scandal. If that politician is the president or a cabinet member, a gaffe can have real-world repercussions.

John Dickerson writes at Slate that when politicians show authenticity — anger, fear, uncertainty, weakness — it often turns into a liability. The vice president, by contrast, offers the power of his personal example: “people can actually use what they see in another person to sustain them in their own lives.”

As much as his candor, his charity and his empathy make Biden an inspiring figure and sadly a rarity in politics, his aren’t necessarily the qualities of a president, however.

Biden knows that. It’s why he’s not running for president a third time.

On the Republican side, former Texas governor Rick Perry also found out that charity and empathy are not all it takes.

Matt Mackowiak relays a powerful anecdote from the last time Perry sought his party’s presidential nomination four years ago at Townhall. During one of the primary debates, candidates were seated around a table and furiously making notes while others were talking to remind themselves of a point they wanted to make.

One candidate, former US senator Rick Santorum of Pennsylvania, noticed that Perry wasn’t writing very much. Through the course of the debate, Santorum told the story of the tremendous health challenges that his daughter Bella, who suffers from a rare disease, had faced through her life. It was a touching story. As the debate ended, the candidates stood up and shook hands. Santorum walked over to Perry and glanced down at his paper and saw just three words: Pray for Bella.

I don’t know how you can read that and not choke up.

When he announced he was suspending his presidential campaign on Friday, Perry said he shared the news with no regrets. As “I approach the next chapter in life,” he said, “I do so with the love of my life by my side, Anita Perry.”

We have our house in the country, we have two beautiful children and two adorable grandchildren, four dogs and the best sunset from our front porch that you could ever imagine. Life is good. And I am a blessed man.

Biden and Perry have both been enormously successful in politics. Although the former joked with Colbert about the respect the vice presidency deserves (very little, he suggested), Biden has been one of Barack Obama’s most important advisors and played a key role in the administration’s relations with a Republican Congress. Before he became vice president, Biden had a long and distinguished career as a senator. Perry has been Texas’ longest-serving governor and seen to it that his state is one of the economically most vibrant in America. Those are proud records and both men deserve (or deserved, in Perry’s case) to be taken seriously as presidential contenders.

But some of the very qualities that make them such good men should also give voters pause about their presidential ambitions.

The American presidency is probably the toughest job on Earth. The power and responsibility that come with it are too much to ask from most people. Like a surgeon who cannot let his personal affection for a patient get in the way of the job at hand, the president of the United States must be able to make life-and-death decisions without personal feelings interfering, or at least not too much.

Scientists say that people cannot do empathy and problem-solving equally well at the same time. A good president has the capacity for both. But when push comes to shove, Americans will often demand a man or a woman who’s better at the latter than the former, as they should.

It’s why former secretary of state Hillary Clinton, for all her perceived lack of authenticity, is still by far the favorite to win the Democratic Party’s presidential nomination next year and why real-estate mogul Donald Trump, despite his high poll ratings, is extremely unlikely to win the Republican nomination.

Americans like their politicians affable and folksy. But few would mistake those qualities for competence.