Not a professional historian but "Americans kept all of their earnings" does not mean there wasnt any tax collected. Tariffs and Excise taxes were far far higher back then than they are now and as I understand collected far more revenue than you might think. Ad valorem taxes (think of the sales tax, a tax that varies on the cost of a good) raised revenue of 6.5% of GDP in 1910. In 2010 the income tax raised revenue of 9.3% of GDP. In other words, the taxes that existed in 1910 did not include an income tax but still collected decent revenues but in the form of tariffs and excise taxes.
This Facebook post is confusing direct/income taxes with every kind of tax, or rather, presuming that the government collected less money in taxes from the people before it collected income tax.
The American government has always funded itself, in part, by money from its people. If you apply some quick logic, you can realize pretty quickly that there are many different ways for a state or country to collect enough taxes to run necessary programs - after all, there are a number of states that currently do not collect direct/income tax, and they all still provide many services to their populations. For basic terminology, direct taxes are those pulled straight out of income/earnings/revenue. Indirect taxes are tariffs (taxes on goods as they enter or exit a territory), sales taxes, property taxes, etc.
The United States government has always collected taxes, but post-revolution, the government wasn't too thrilled with the idea of imposing direct taxes, and the Constitution required that any taxes collected by the federal government to be proportional to a state's population. The new government still needed money, though, and so collected tariffs on certain high value goods (like whiskey and glass). New expenses (war, namely) led to a greater need for government funds, and so the government continued to impose further taxes - on property in the 1790's and then, drumroll... on income, during the Civil War. The Revenue Act passed in 1861 (and the I.R.S. was created!) and the government began collecting direct taxes on incomes over $800/year. This lasted for a decade before being rescinded in 1872. Another income tax law was passed in 1894, then was ruled unconstitutional (for not taking into account states' populations) a year later, but Americans and the government began to realize the necessity of direct taxes.
And so the 16th Amendment, which allows for direct taxes to be levied by the federal government without regard to state population, was passed in 1909 and ratified in 1913.
Info from the Library of Congress and a Forbes article.
It is true that before then there were no federal income taxes. There were other taxes, though, mostly in the form of Tariffs, excise taxes, sales taxes, etc.
The other part of the statement, though- that we still had schools, colleges, railroads, subways, an army and navy, etc, and therefore taxes are unnecessary- is a little disingenuous. 1910 was a very different time. The government needs much more money now, but it also does a lot more with it.
We had schools and colleges then, but school wasn't compulsory until the 1920's, so you didn't need as many of them. Schools today are also more expensive, due to the need to teach a broader range of skills and maintain more expensive equipment and buildings.
Railroads have a rich history in and of themselves, but I hope I'm not generalizing too much when I say that there were many 19th century railroad company monopolies and that they were rather abusive at times. The statement above also ignores how their economies have changed. What might have worked then might not work now in a world with competition from cars and planes. Or if it did work, it might not be priced competitively enough to remain within reach of poorer Americans. As for subways, they were still in their infancy, the first one in America being built in Boston in 1897. And since then, their construction and maintenance have grown more costly as the systems grow, more parts need replacing, and urban density increases.
As for army and navy, that's extra disingenuous. Before the 1910's, with WWI and the introduction of the income tax, the US military was a very different beast. We had no real standing army, and our navy was not as strong as many other naval powers. Before the 20th century, all you really needed for an army was to draft a bunch of young men and hand them rifles and a few cannons. But modern war required a lot of expensive mechanization that in some cases would then be rendered obsolete within a decade or two by the pace of technological progression. Today most militaries rely on a professional standing force ready for rapid deployment, which is a whole lot more expensive to maintain than a force that relies on conscription and several weeks to mobilize.
Finally, while this skews a lot more heavily into AskEconomics than AskHistorians, there's also the negative effects of tariffs on free trade. Without free trade we'd be without a lot of the benefits of globalization, and you'd see many commodities be priced unreasonably high, and many businesses fail due to not being able to be competitive on the global market.
Basically, you could go back to a 19th century tax model, but it would require cutting spending back to 19th century levels as well, and that would require regressing towards a 19th century standard of living. And in the end you'll still likely be spending a lot of money on taxes, they'll just be in other forms.
Before WW1, defense spending was about 1% of GDP, and we had no Social Security, Medicare, or Medicaid. Today, we spend about 5% of our GDP on defense and another 10% on Social Security, Medicare, and Medicaid. We pay more, but we also get more. Federal revenue (from all forms of taxes and levies) in 1913 was about 4% of GDP, and today it's about 19% of GDP - the difference is just about the cost of increased defense spending, Social Security, Medicaid, and Medicare. All the other great stuff we get like NASA and National Institutes of Health come from improved efficiency - we actually get a lot more bang for our buck than they did back then.
It is important to note, in addition to the other excellent comments here, that the government has expanded the services it provides since 1913.
This primarily happened around the time of WWII, when an increase in social spending led to a correlating jump in tax revenues. Since 1952 or so, we've collected taxes at a rate of between 18-22% (usually) of gross-domestic product. Spending always jumps during wars, but before WWII (and after WWI) it was usually around 5-10% of GDP. Since then it has been between 18-25%, depending on wars and recessions (when stimulus packages have increased spending).
What do we have now that we didn't have then?
For one, social security. That didn't exist before 1935, and it was amended in 1939 and again later on. This was a significant source of both revenues (people pay into it, after all) and expenditures (people take out of it, as well).
We also have unemployment insurance, an automatic stabilizer that, during recessions, keeps people from being completely destitute and which can help minimize the recession by keeping consumption higher than it might otherwise be (that's the theory anyways).
We have welfare benefits now, particularly for the handicapped and needy children, that weren't present before FDR to the extent they were after him (if at all).
Just a few examples.
FDR's changes were not alone: Truman had some of his own, the establishment of Medicare under Johnson was important (entitlement spending on Medicare/Social Security have gone up as a percentage of GDP and budgets over time). And not all of FDR's programs lasted or were even necessarily good. But when we talk about the overall level of poverty among the elderly, of automatic stabilizers that help the economy during recessions, of redistribution programs that help the poor through higher taxes on the wealthy, a decent amount of them are only possible because we tax more than we used to.
Can someone link the text in question?
Regarding the railroads. It's true that a permanent income tax wasn't established until 1913. But it's not as though that would be an alien concept to most Americans because they had paid an income tax before. The Revenue Act of 1861 established a flat rate income tax. The subsequent Revenue Acts of 1862 and 1864 changed it to a progressive income tax and created the IRS to collect it. The Act of 1862 mandated that the income tax would expire in 1866. So, it was temporary. However, the key point is Lincoln was the one who funded the initial creation of the intercontinental railroad with the Pacific Railroad Acts of 1862 and 1864. He provided bonds (loans) to the companies to build the railroads (this was greatly desired by California where people wanted to be able to visit relatives on the East coast and Lincoln wanted California to remain loyal to the Union). So, the railroads were initially built using federal money and the money partially came from an income tax. As well as things like the excise tax. This money was also used to fund the army and the navy. There was practically no interstate highways or roads to speak of.
Some of these things (like subways or in state roads) were built by the states. States began creating or increasing income taxes beginning in the 1840s and more and more did so through out the 19th century. States used different models and rates and not all of them did it. But the states you associate with highly developed roads and sophisticated subways did use state income tax funds to pay for them (among other sources of income).
There were almost no interstate highways at that time, schools were not what they are today, colleges were smaller because they were often restricted (either explicit restrictions on black people and women or implicit restrictions based on criteria to get in that most people couldn't meet). It's fair to say that very few of us would prefer to live in 1913 over the current day.