Because it's important to understand how we got to where we are. I admit that it doesn't really matter what Pharoh built the pyramids or who led the Germans in the Battle of Teutoburg Forest (Arminius, by the way. I've had plans to write a historical fiction book on him for almost three years, haven't written a word), but it is important to know that Germany was never under Roman control, which is the result of the battle of Teutoburg.This alone created a culture gap in Europe which is still prevalent, although now it's much smaller then before.
The easiest way to think of why we need to learn it, though, is to not pull it back so far. Is it important to know what happened yesterday? The same reasons that it is important hold true for right now.
So, lets use that example. It's obviously very important to know that we where in Iraq fighting a war yesterday. So it's important to know that we invaded Iraq in 2003.
To know why we where there, it's important to know about the War on Terrorism, and 9/11. Which then leads us to US presence in the Middle East, which then leads us to why we where and are there. It's important to know about the Iraq-Iran war in the 80s, which lead us further back into the general history of the area. We have to know about Islam, about the different groups, and what conflicts they have. Simply saying "so we learn from past mistakes" is the same as saying that "E=mc2" is just an equation. It's true, but so much is covered by those phrases that they're inadequate at describing it.
We support Isreal. Why? I'm not going to do another connect the dots, but that leads us over a thousand years back alone. Same with why the Republicans control the south and the Democracts control the North, why the South is Evangelical while the North is not, why is there a UN, all of those things are decided by history, and if a person expects to be able to add himself into the world, those are things he need to learn.
Unless you plan to be an idiot who has no idea about what's going on with the world, and has no say in what his government does, learn your history.
Lord Acton said "the science of politics is the one science that is deposited by the streams of history, like the grains of gold in the sand of a river; and the knowledge of the past, the record of truths revealed by experience, is eminently practical, as an instrument of action and a power that goes to making the future.\"