some cases, slavery, even for the majority of soldiers who didn't come from slaveholding backgrounds. 

In both armies, however, many soldiers were simply fighting for what soldiers have probably always fought for. They wanted to stay alive and to help their friends. The bonds formed in combat were as strong in the Civil War as in any other conflict. It is also important to remember that, by the end of the war, a majority of soldiers in both armies were conscripts who probably didn't feel that they had much at stake in the war. Major cities in both the Confederacy and the Union experienced draft riots, and as the privations of the war grew worse, scores of Confederate soldiers simply deserted and went home, an offense that was punishable by death.

There are many answers to your question.  However, the simplified view is that the south was fighting to protect their economic livelihood which at the time was slavery.  The industrialized north was fighting against slavery which they saw as an inhumane institution.

With that being said, you could begin by looking at the governmental clash with the issue of slavery.  In the Constitution, you have in Article II listed that slaves were counted as 3/5 of a person for representation purposes only in the House of Representatives.  You also have the various compromises authored by Henry Clay, such as the Missouri Compromise and the Compromise of 1850. These compromises were about keeping the status quo and not tipping the balance of slave states and free states. Even in Kansas, there was an outbreak of violence over slavery, which many historians call Bleeding Kansas. It was an attempt to stack the deck in voting for or against slavery and the settlers, both from the north and south,  to the region fought over their beliefs about the issue of slavery.  John C. Calhoun with the Nullification Crisis tried to set the south up to be able to over turn or nullify federal law.

The industrialized north was concerned with the mistreatment of slaves. However, the north really did not treat its workers much better than the southern slave owners treated their slaves. The industrialized north had poor housing, low wages, and long hours for their workers; the only difference was the north did not beat their workers. For the north was about protecting the Union and stopping the mistreatment of the slaves.

A great document to look at is the South Carolina Secession Statement.  Which you can find at the civilwar.org website.  Here is what Calhoun wrote about South Carolina and he used the words of the Declaration of Independence against the Union.  He stated, "...A struggle for the right of self-government ensued, which resulted, on the 4th of July, 1776, in a Declaration, by the Colonies, 'that they are, and of right ought to be, FREE AND INDEPENDENT STATES; and that, as free and independent States, they have full power to levy war, conclude peace, contract alliances, establish commerce, and to do all other acts and things which independent States may of right do.'" Calhoun believed that war was the only way to protect the southern way of life - slavery.

It is easy to say that the Civil War began and ended with the issue of slavery; however, the slavery reason in recruitment did not reach its peak until Lincoln issued the Emancipation Proclamation.  This happened well into the war and was used brilliantly by Lincoln to keep European Countries from siding with the South.  (The major countries in Europe were giving up or had given up slavery in the past century and were putting pressure on the United States to follow.  Once the Emancipation Proclamation was given, European countries couldn't side with the South without legitimizing slavery.)  It also served as a rallying cry for abolitionists to join the military (Though even then their numbers were considerably lower than that of Irish and German immigrants. [See below.])

So, if the major reason wasn't slavery- why were the soldiers fighting?

Let's start with the South:

First, not everyone owned slaves in the South.  Below is from the 1860's census:  It lists the percentage  of white households that owned slaves.   In general, slavery was not an aspect of the daily lives of most southern citizens.  

The majority of soldiers were fighting against what was called "Northern Aggression."  In other words, they were fighting against Federal control of the States.  (It's basically going back to the Constitutional Convention and the argument over Federal oversight.)  The South felt strongly that the 10th Amendment applied in regard to the slavery decision- In other words, since the Constitution did not give the authority to decide on whether slavery was right or wrong to Congress, according to the 10th Amendment, the states should decide based on popular sovereignty.  For the South, Congress (which at this time was on the brink of being controlled by abolitionists) had been checked by the previous Presidents who had basically upheld the 10th Amendment as the reason for slavery in the U.S.- Pierce and Buchanan notably, but the tradition goes much further back.  

The 1860 election of Lincoln put Congress in a much better position of abolishing slavery.  For the South this meant that the Federal Government was going to push Federal oversight and force the removal of slavery in the Southern States going against popular sovereignty and the 10th amendment.  This was unacceptable in the South.  They held that the 10th Amendment was being violated, and they would not let it stand.  Rather than give up their rights as states, they chose to break away from the Union.  When the North "invaded"-- Southern Soldiers enlisted--not to keep slavery but to protect the rights of their states to determine their own interests.  

A good example of this is Robert E. Lee.  Robert E. Lee was opposed to slavery.  Read the letter he wrote to his son on the subject: http://www.civilwarhome.com/leepierce.html.  Lee was invited by Lincoln to lead the Union Army.  He declined, choosing instead to support his home state, his relatives, and neighbors in Virginia.  He was not alone.  Many journals from the South show southern farmers who do not like the establishment of slavery, fighting for the South due to State Rights issues.    

For Northern soldiers some did fight to free the slaves.  This was largely tied to religious beliefs found in the more Puritan states where the inhabitants felt that slavery was *morally* rather than politically wrong.  Many of the early enlistments from the middle states were also tied to the sense of patriotic duty to the United States.  The ideal of keeping the country together through the military was not new.  During Presidents Jackson, Harrison, and Taylor the South had threatened leaving the Union; however the military was enough to keep them in line.  Last, like today, military service was a monetary benefit to struggling farming families where sons could fight for the country and send the money home to help their parents.  

It is important to note that African Americans in the North were forbidden to enlist until two years into the war.  Once the Emancipation Proclamation was established, several adjustments to the laws forbidding African American enlistment were put in place and the African American soldier count began to rise.  

  However a good percentage of Northern Soldiers were German and Irish Immigrants right of the ship.  Approximately 200,000 German immigrants fought in the Civil War and 170,000 Irish.   These soldiers had little to no abolitionist or political entanglements.   They fought for societal acceptance and many fought for a patriotic idealism that broke them away from the injustices of their old countries.  Joining the war was also practical.  It gave them food, shelter, and money to support their families.  

As for Congress-- It is important to note the importance of the South to the economic health of the United States.  The South due to the Cotton Boom was one of the more wealthy areas of the world and was collecting a great deal of money.  The United States needed the South in order to remain financially stable.  (Ironic that the Civil War will squash the Cotton Boom and send the South into an Economic Depression while the North headed into an industrial boom.)  Because of this, Congress will put considerable effort into recruitment offering incentives, land grants, etc in order to pursue the unity of the United States while achieving freedom for slaves.

It is possible to give a variety of answers to this question.  Over the years, scholars have answered this question in different ways and it is impossible to know which answer your instructor expects of you.

The main reason why scholars have answered this question differently over the years is that there is such a wealth of evidence about what the combatants felt they were fighting for.  Historians have literally tens of thousands of letters written by soldiers from the Civil War that they can examine for evidence.  When you have that many letters, written my thousands of different people, you can find support for different hypotheses.  In this answer, I will present two main theories about why soldiers fought in the Civil War.

One theory holds that soldiers in this war fought for the same reasons whether they were from the North or the South.  Those reasons had nothing to do with ideology or beliefs about government, rights, or slavery.  In this view, soldiers fought because they did not want to let their comrades down.  They fought because they did not want their fellow soldiers to be killed and because they did not want their fellow soldiers to feel that they were cowards.  For scholars who adhere to this theory, the soldiers on either side were fighting for their close comrades, not for their countries.

A second theory holds that ideology was actually very important to these soldiers.  From this point of view, the soldiers from the North fought to preserve the union.  They felt that they were fighting to ensure, as President Lincoln said, “that government of the people, by the people, for the people shall not perish from the earth.”  The Southern soldiers, too, were fighting for a cause.  They felt that they were following in the footsteps of the Founding Fathers.  They were fighting for the right of self-government.  They were fighting to uphold a system where the people of a given state could rule themselves, rather than being ruled by some far-off federal government.

Thus, we have two very different theories about what the combatants on each side felt they were fighting for.  Please consult your course materials to find out which theory your instructor believes in.

First, we must acknowledge that we cannot know what the average soldier believed because we do not have anything like opinion polling from the time.  Different soldiers certainly fought for different reasons, with some fighting because they had to, others for adventure, and so on.

In general, though, we can say that most Union soldiers were fighting to preserve the Union and most Confederates were fighting for the idea of states' rights.  The Confederates felt that their rights were being infringed upon by the federal government and wanted to break away.  The Union soldiers believed in the idea that the South had no right to break away.