No one tests the historic optimism of the American people quite like your average politician. Poll after poll finds a deep distrust of government, with more than two-thirds saying they can’t believe what they hear from Washington.

You don’t have to look far for examples of why they feel this way. Americans have learned to be wary of taking what politicians say at face value. You could mine almost any political speech for examples, but consider some of the claims from President Obama’s latest State of the Union address.

He brought up the wage gap between male and female workers, adding that women “make 77 cents for every dollar a man earns.” This implies deliberate discrimination.

The fact is that the average woman tends to make different lifestyle choices when it comes to decisions about where and how much to work, making direct comparisons flawed, to say the least.

Worse, as The Washington Post’s fact-checker columnist noted, the president is using a figure that makes the gap look the widest: annual wages from the Census Bureau.

Because women tend to work fewer hours, weekly or hourly wages would be more accurate, and — not surprisingly — they show a much smaller gap.

When it came to foreign policy, Mr. Obama touted the fact that U.S. troops are out of Iraq.

Here, the problem is one of omission and context. Yes, he may have withdrawn U.S. troops from Iraq, but that doesn’t mean (as the president hints here) that the country is safe and the mission is completed. On the contrary, violence is on the rise. Nearly 9,000 people died in 2013, a five-year high.

Meanwhile, al Qaeda is resurging in Iraq, erasing many of the gains U.S. troops had made in securing the cities of Fallujah and Ramadi.

Small wonder that the Obama administration has been downplaying the “security consequences of its abrupt pullout from Iraq after it bungled negotiations to extend the presence of a small U.S. force to advise, train and support Iraq’s fledging military,” writes Heritage Foundation Middle East expert James Phillips.

When it comes to fiscal responsibility, Mr. Obama simply stated, “Our deficits — cut by more than half.” Sounds impressive, but again, it’s not the whole truth.

He didn’t mention how high the deficit was to start with: During his first term, the deficit exceeded $1 trillion for four years in a row and reached its highest level as a percentage of gross domestic product since 1946.

Nor did he dwell on the fact that programs such as Obamacare are set to send future deficits soaring. As Heritage budget expert Romina Boccia noted after the speech, thanks to his signature health law, Mr. Obama is “leaving it to a future president to solve an even bigger fiscal mess.”

The president also took credit for “a rebounding housing market.” He could have added that he’s called for ending Fannie Mae and Freddie Mac, the two government-sponsored enterprises that distorted the market and played a big part in inflating the housing bubble.

The problem is the Senate is considering legislation that would replace Fannie and Freddie with a new government agency called the Federal Mortgage Insurance Corporation.

The FMIC, Heritage’s Norbert Michel has pointed out, would be a federal regulator and insurer of mortgage-backed securities. In other words, meet the new boss, same as the old boss.

“As president, I’m committed to making Washington work better, and rebuilding the trust of the people who sent us here,” Mr. Obama said.

Speeches that cherry-pick facts that flatter and omit the ones that hurt — speeches that present facts out of context — have the opposite effect. They increase that lack of faith.

Until that changes, Americans would be well-advised to apply President Reagan’s famous dictum on the Soviet Union to their own elected officials: “Trust, but verify.”

 - Ed Feulner is the founder of the Heritage Foundation