What are some of the biggest lies in history that are still being taught in modern day schools?

The idea that Columbus set out west from Spain to prove that the Earth wasn't flat (as everyone supposedly thought) and that he discovered the continent of North America.

Everyone at that time with any education knew the Earth was round. The Greeks had calculated the size of the Earth long before with a reasonable degree of accuracy. People doubted Columbus' expedition because, had the Americas not been there, he would have run out of supplies long before reaching Asia.

Columbus never set foot on the continent. He landed in what's today known as the Bahamas.

The Viking explorer Leif Ericson  had reached modern Canada 500 years earlier- there's a confirmed Viking camp at L'anse aux Meadows. Never mind that the native population already knew it was there.

Even worse is that Columbus is hailed as some sort of hero in the USA, when he was actually a fairly nasty piece of work. Like 

That the "Middle Ages" and the "Renaissance" existed in the sense that is commonly given to them.
To call someting barbaric "Medieval" is preposterous for example. Compared to the "modern world", it was an era of religious tolerance.

Just recently, I spoke to a friend who talked about how much farther we’ve come in terms of the human lifespan and said that the old men in any given city in America in the 19th century would be in their forties.

Many history teachers confuse the average for the whole variance. They deduced that the mean or median age in a particular period of time being forty, or fifty, meant that that was the actual lifespan of a given adult in a town.

The problem, of course, is child mortality. Ancient societies had very high rates of infants and young children dying due to disease, accidents, injuries, violence, famine, and other issues. Moreover, as a result of these issues, women in traditional societies frequently had to give birth many times, just to insure that any children would survive to adulthood (let alone enough children to insure the prosperity of the family). As a Live Science article summarizes,

Discussions about life expectancy often involve how it has improved over time. According to the National Center for Health Statistics, life expectancy for men in 1907 was 45.6 years; by 1957 it rose to 66.4; in 2007 it reached 75.5. Unlike the most recent increase in life expectancy(which was attributable largely to a decline in half of the leading causes of death including heart disease, homicide, and influenza), the increase in life expectancy between 1907 and 2007 was largely due to a decreasing infant mortality rate, which was 9.99 percent in 1907; 2.63 percent in 1957; and 0.68 percent in 2007.

But the inclusion of infant mortality rates in calculating life expectancy creates the mistaken impression that earlier generations died at a young age; Americans were not dying en masse at the age of 46 in 1907. The fact is that the maximum human lifespan — a concept often confused with "life expectancy" — has remained more or less the same for thousands of years. The idea that our ancestors routinely died young (say, at age 40) has no basis in scientific fact.

With those problems largely resolved, the average lifespan did indeed explode upwards, but not because people were living that much longer in terms of the maximum lifespan. If you go look at gravestones for the 18th and 19th centuries, you will see plenty of people in their seventies, eighties and nineties. And, of course, as societies industrialize and women get opportunities outside of the home, population growth tends to plummet, with most people choosing by preference to have only one or two children, leading to net zero or even negative population growth.

Is ongoing medical advance useless? Of course not. For one thing, I have no doubt that people will usefully begin living easily into the triple digits, with many reaching 120 to 140. For another, even if that doesn’t occur, what will occur is that quality of life will improve. Gerontological care may not have made the elderly life very much longer on average, but it sure as heck made that living less painful and more functional. And if we can resolve Alzheimer’s and other neurodegenerative disorders, we’ll make it so more and more elderly adults live their last decades on Earth completely in charge of their faculties.

I suspect that we’re probably at the point where we’re not going to see too much improvement in lifespans from mere social improvement. Yes, there are major inequalities that still remain, and we’re going to improve a lot on issues like pollution, lead contamination, heavy metals of all kinds, and so forth. But, barring global warming being truly insoluble, these efforts will plateau in the near future.

But the reality does remain that, historically, it was the death of children that kept societies’ average lifespan so abysmally low, and it took major collective social improvements, not just individualistic technological and medical care advances, to really see human care improve. And history teachers who indicate otherwise are unwittingly advancing a particular individualist, scientistic, pro-capitalist agenda.

A great example on the topic can be found in Lewontin’s analysis of tuberculosis, worth seeing in his review of Lewis’ book on TB. Noteworthily, even Lewis, who thinks that chemical treatments certainly had some effect, grants readily that “There is no doubt that major changes in our mortality from infectious disease in general have occurred over the past two centuries, long before the sulfonamides and penicillin, and it is quite likely that these benefits came along with improvements in the standard of living in the western world, perhaps by improved nutrition as he suggests, perhaps also because of better housing and sanitation and less crowding. We are rid of typhoid and cholera in this country largely because of modern plumbing”. I think Lewontin is making a point that is strong in order to drive home a more political point while Lewis is mostly agreeing but being less of a polemicist, and that’s essentially the state of medicine on this dispute. Many people engaged with this response as if the claim is controversial, but Blum’s model is fairly well-accepted and it puts medical care dead last as a causal driver of the development of a disease.

Some people came to the New England colonies seeking the religious freedom to discriminate and oppress anyone who did not share their religious views. Parts of two different colonies were founded by people driven out of Massachusetts Bay Colony because of the residents of Massachusetts Bay Colony wanting to exercise their religious freedom to hang people of differing religious views.
Roger Williams was driven out of Massachusetts Bay Colony for the "crime" of being a Baptist - and founded Rhode Island.
Some of my ancestors helped found Waterbury, Connecticut because they had been driven out of Massachusetts Bay Colony for the "crime" of being Quakers.

For those who refused to leave Boston or Massachusetts Bay Colony, their fate was different. Mary Dyer, was hanged on the Boston Common in 1660 for the "crime" of being a Quaker by people who came to the colonies for "religious freedom"