I think Alexander meant that Malvern Hill would have never happened if Lee's plans would have been followed correctly early on in the Seven Days Battles. If the advantages early on would have been exploited, he believed they would have routed them before Malvern Hill.
Exactly. Glendale/Frayer's Farm was supposed to be the final battle. Lee had the perfect set up to split McClellan's army in two. If everything had worked according to Lee's plans,*Malvern Hill would never have happened.
Building on diane's post, the exact orders that Lee gave Jackson that morning are still a mystery. That they are a mystery could explain why Jackson did not completely understand them. That and perhaps he was too proud to admit it was not clear as to what was being asked of him. Based on*the events that unfolded that day, it seems that Lee told Jackson to engage the Union rearguard at White Oak Swamp and prevent them from being able to provide reinforcements.*
The Union rearguard under Franklin engaged Jackson's division in an artillery duel across the swamp near the ruined bridge. In that regard, by drawing Franklin's attention, Jackson was successful. According to John S. Salmon, Hampton told Jackson that the swamp could be bridged, but only for infantry. Jackson told Hampton to build his bridge. When Hampton returned to inform Jackson, he was met with silence. Jackson decided he could not counter the Federal guns without the necessary artillery as Franklin's command was too strong. Jackson and his four divisions did not proceed any further. There was no infantry engagement at the Battle of White Oak Swamp. Due to Jackson's inaction, a group of reinforcements were detached from Franklin's division and helped to reverse the gains made by the Confederates at Glendale. That night, the rest of Franklin's division moved to join the Federal army at Malvern Hill. In that regard, Jackson was not successful.
As with the general consensus, I think exhaustion combined with the stress of war is the culprit. At White Oak Swamp, the Confederate casualties were 15, three of them fatal. It is estimated that the Federals suffered around 100 casualties.*Imagine if Jackson had been more than partially successful at White Oak Swamp and pressed on despite his misgivings. The casualty comparison seems to imply that strength was definitely on Jackson's side. This is evident when visiting the site today as it is clear the Federals occupied a higher position. Such a position should have minimized their casualties as would be the case the next day at Malvern Hill, though the position there was stronger and equipped with overwhelming*artillery. If Jackson had followed through and joined the battle at Glendale on the 30th, we might not be talking about the end of the war, but a profoundly weakened Army of the Potomac that bypasses Malvern Hill and presses on to Harrison's Landing.
Assuming then that the events which followed the Seven Days occurred as they did (Confederates still win 2nd Bull Run) you can then pontificate what may have happened at Antietam as the Confederates would have been up against a far more demoralized Army of the Potomac. With such a psychological advantage, would the Confederates have stood a better chance? If so, would Antietam have been the Union's Appomattox? Would the discovery of the battle plan wrapped cigars have made any difference at that point?
Considering what had been asked of Jackson prior to and during the Seven Days, which I think we can all agree was a lot, he and his men were exhausted and he likely felt it was time for others to step up their game. That may not have been typical of Jackson's personality, but this was clearly not the same Jackson. Some did, Longstreet and A.P. Hill breaking through the Union line, and others did not, Huger playing into Slocum's trap by dragging his feet on Charles City Road. Huger's action, or lack thereof, mirrored Magruder's cautiousness from the previous day at Savage's Station. It can be argued that it is Huger who really ruined the day as he was to strike first and have his divisions supported by Longstreet and Hill. Lee was waiting with Longstreet listening for the sound of Huger's guns. They heard guns but the sound was too distant, which means Lee heard Jackson's guns at White Oak Swamp. At practically the same moment, as if out of some sort of bad dream, Jefferson Davis arrives at the front complete with an entourage. This was a distraction for Lee who was trying to figure out what was happening. It all plays out like a comedy of errors.*
In his own way, Jackson did his part, just not in a way that resulted in a resounding win for the Confederates at Glendale.*
Reference:*
The Official Virginia Civil War Battlefield Guide
John S. Salmon, 2001