Even the pope claims to be infallible only on matters of faith and doctrine.
On the chance of rain or the speed of a racehorse he will freely admit that he is just as fallible as you and I. Whereas secular dictators, and especially ones who are building a personality cult, are implicitly claiming to be infallible about everything.
This is quite a burden, although it helps that dictators can deny things have gone wrong, and punish anybody who says otherwise.
Nevertheless, sooner or later people are bound to notice that things really have gone wrong. That is President Xi Jinping's main problem at the moment, but it is also China's.
For more than two years now, Mr Xi has loudly proclaimed that China's zero-Covid policy has been a brilliant success that demonstrates the superiority of the Chinese system and of his own leadership. And for a while there, the evidence was on his side.
The Covid death toll in China is still under 6,000, while Covid fatalities in the United States, with only a quarter of China's population, are nearing the million mark. However, China achieved this miracle only by almost completely shutting its borders and imposing draconian shutdowns on entire cities at the first sign of an infection.
That succeeded for a while, just as it did in Australia and New Zealand, two geographically isolated countries that followed essentially the same policy. But their governments knew that this could not be a permanent policy, and as soon as the great majority of their populations were fully vaccinated they began to release the restrictions.
Happily, by then the Omicron variant was taking over, making Covid even more infectious but far less lethal, especially for vaccinated people.
Xi Jinping seems to have missed that memo, and has pressed on with the zero-Covid policy even at great cost to the Chinese economy and in the face of growing resentment among ordinary Chinese people.
At the moment, 340 million people, around one-quarter of the population, are under full or partial lockdown in 46 different cities. The 25 million residents of Shanghai, China's commercial capital, are in their fifth week of lockdown.
Guangzhou, the southern industrial hub, has ordered the mass testing of 5.6 million people after the detection of one suspected Covid case.
Even Beijing is teetering on the brink of lockdown, with schools already closed and people panic-buying provisions for what could be another long confinement to their homes.
Given the huge infection rate of Omicron -- in both the United States and the United Kingdom around 70% of the population have had Covid at least once -- this policy cannot logically have a long-term future.
The ceaseless lockdowns are hitting China so hard that second-quarter growth in an economy that used to boast of 10%+ growth rates is forecast to be only 1.8%. This means not only unemployment and potential unrest, but Chinese customers elsewhere shifting away from dependence on supply chains originating in China. The shift could be permanent.
And yet Xi Jinping perseveres with the policy. His regime has not even speeded up vaccinations in China, although fewer than half the over 60s have even had one booster shot. Nothing must be allowed to suggest that the zero-Covid policy is failing. Why?
Because an absolute dictator must appear infallible. Mr Xi has boasted so much of the "success" of his victory over Covid, made it so much his own signature achievement, that no doubt can be admitted -- especially at a time when he is planning to make his dictator-for-life status official.
This autumn marks the end of the two five-year terms that Mr Xi would have been permitted under the Communist Party's post-Mao rules, which were designed precisely to thwart other would-be absolute dictators from gaining powers.
His plan was to be elected to a rule-breaking third term at the 20th National Congress of the Chinese Communist Party next October or November, and even a year ago he looked like a shoo-in.
Mr Xi has purged and/or jailed a great many senior officials on corruption charges, and those who were still in office seemed thoroughly cowed.
Nevertheless, there are still a lot of senior Party people who think that one-man rule is always a mistake.
You'd still be unwise to bet against Mr Xi's chances of a third term (and as many more as his lifespan allows), but he himself is now running scared. Which probably means that there will be no change in the current, crazy Covid policy at least until the end of the year.