There are actually some very good answers from flaired users that can go into greater detail than I can. I'll try to find them but I'll give you a more general run down.

The Civil War generals that had gone to West Point had been schooled in the method of Jominian warfare, named after Antoine-Henri Jomini. He fought in Napoleon's army and truly grasped Napoleon's style of warfare. This called for a decisive battle to completely eliminate the enemy army as a functioning fighting force.

However, even though Civil War generals sought this decisive battle they were unable to succeed for a number of reasons. One of these reasons was the lack of heavy cavalry in the pre-war American military. What cavalry they did have was essentially mounted infantry and was in relatively small numbers. It was a scouting and screening force that was unable to press advantages like European heavy cavalry had been able to. European nations had military owned and operated stables to breed and train the horses needed for heavy cavalry units. Soldiers were trained in these tactics and trained with these horses. Without heavy cavalry ACW armies were unable to press their advantage at the end of the battle. The advances in firearms technology had also severely weakened the effectiveness of cavalry.

The pre-war American military was also much smaller than the military during the war. Winfield Scott, the highest ranking general, had experience with at most ~10,000 men in Mexico. Compare that to the hundreds of thousands of men involved in many of the ACW battle. Both sides were basically learning on the fly when it come to commanding large amounts of men.

Edit: This comment does a fantastic job of explaining it far better than I ever could.