General Lee was a fine soldier and a good and decent man, but he was afflicted with “Victory Disease”. He couldn’t accept anything other than his army would carry the day. And, he didn’t listen to Longstreet and flank the Union lines past Big Round Top, because he believed that his troops could punch through the Union lines.
Actually---I know I'll get flamed here---Lee was not quite as great a general as he is always cracked up to be. In "Attack and Die," historians Grady McWhiney and Perry Jamison note that in 11 of the first 12 battles (including multi-day battles) of the Confederacy, the Union only had a higher casualty ratio of all men deployed in battle in one: Fredericksburg. Admittedly, Shiloh, Vicksburg, and a couple of others on their chart were in the West; and 1st Manassas was not Lee's command. But still, even in all those battles Lee led the South, he only achieved a superior
ratio of casualties inflicted on the enemy at Fredericksburg. His losses at Antietam and Gettysburg were horrendous, over 20% of his force at Antietam and 30% at Gettysburg.
For a general leading the side that supposedly is "playing defense," this is an unacceptable level of loss, one doomed to defeat.