It seems to me that you can sort of see McClellan's objectives as being:
- Avoid another Second Bull Run
- Avoid letting Lee go after Washington
- Drive Lee out of the North
- Relieve Harpers Ferry
- Do heavy damage to Lee's army
- Kill Lee's army
And the operational scheme is based on this.
In the early phase of the campaign McClellan is moving out of Washington in corps line abreast, leapfrogging forwards in case he comes into contact with the enemy. Stuart's screen is still around and east of Frederick until late September 12th, and indeed Lee himself doesn't march out of Frederick until September 10 (main body) and 11 (DH Hill). This is an advance to contact because Lee might be waiting to draw McClellan into a major battle, and at this point McClellan's force with his army is a bit more than 80,000 PFD (about 85,000 once Weber's brigade has joined, remembering that several regiments haven't yet and nor have Morell and Humphreys) - which is within the brackets of his estimate of Lee's strength. As such at this point McClellan thinks it important to have his whole force able to fight on contact.
Once Frederick is liberated and SO191 found (afternoon of the 13th), the conditions change. McClellan now knows the Confederates are marching divided, and so he pushes his force through to South Mountain where the attack begins on the Rebel rearguard.
There is the scope on the 14th for McClellan to fulfil several objectives at once:
End Lee's invasion of the North - if most of Lee's army is south of the Potomac and McClellan can cut it off from joining the portion north of the Potomac, the continued operation of a small Confederate force in Maryland and Pennsylvania is untenable. This means breaking through at least one South Mountain gap.
Relieve Harpers' Ferry and do heavy damage to Lee's army - if Franklin's wing can break through at Crampton's Gap, there is the prospect of trapping McLaws' wing in the Pleasant Valley (especially if the Harpers Ferry garrison is holding the Maryland Heights) which means about ten of Lee's brigades could be captured. (McClellan probably doesn't know the exact number here but it's two divisions.) This would also allow for the relief of Harpers Ferry.
There is however no scope to kill the Army of Northern Virginia because a significant chunk of it (Jackson's wing, Walker's division) are south of the Potomac (and thus immune to attack). McClellan would have known from SO191 that there was one "command" and one "division" (Longstreet and DH Hill) north of the Potomac and one of each (Jackson and Walker) south of it; Longstreet's "command" is at Boonsborough (actually Hagerstown) and could evacuate via Williamsport or the Shepherdstown fords if that was felt vital.
As things actually developed, the South Mountain Gaps were broken through but Harpers Ferry surrendered and McLaws' wing was able to get out of the trap.
The 15th sees a pursuit where Longstreet's wing pulls back behind Antietam creek, and then Lee goes firm (and stays there over the 16th).
Looking again at the list of objectives, McClellan can now throw 1st Corps across the road north of Sharpsburg (the Hagerstown road) and that's all he really needs to do to end this part of Lee's invasion of the north. Lee however might have one of several plans:
- he might be planning on concentrating his whole army at Sharpsburg and moving north by cutting through McClellan's right wing.
- he might be planning on moving south of the Potomac and then re-entering Maryland, either via Harpers Ferry or via Williamsport.
- he might be planning on having Jackson make a run at Washington, either with this part of his army still at Sharpsburg or not.
If this part of Lee's army retreats over the river, McClellan only needs a small part of his army to stop them re-entering here and he can then aim to hold the line of the Potomac. But if this part of Lee's army doesn't do that, it could be acting as a fixing force (while the rest acts as a turning force) and tie up too much of McClellan's army to respond to a Williamsport movement. (Couch is blocking a Harpers Ferry movement - originally it was all of Franklin but McClellan pulled in Slocum and Smith.)
This I think leads to the logic that IF a major part of Lee's army is not at Sharpsburg THEN McClellan might actually feel required to attack it (to thus defeat it, and free up troops to respond to whatever Lee's next operational movement is). Meanwhile if most of Lee's army is at Sharpsburg then an offensive not conducted a l'outrance has the prospect of doing damage (and possibly more if the 9th Corps movement comes off) while since most of Lee's army is there there's not as much risk of a wide ranging movement.
This is the insight I wanted to mention. If you assume that McClellan did think that Lee's army was about 100,000 (pre-straggle), then:
- If ~30,000 (30%) of Lee's men are at Sharpsburg and 70,000 elsewhere, crush them quickly so you can respond to what the 70,000 are doing. It's a serious blow but not a crippling one to Lee's army (it's still ~70% intact), but the important thing here is to free up the troops.
- If ~50,000 of Lee's men are at Sharpsburg and 50,000 elsewhere, you have the prospect to inflict massive damage on Lee's army and you can free up troops to respond to what Lee is doing with the other half.
- If ~70,000 of Lee's men are at Sharpsburg and 30,000 elsewhere, there isn't really as much of a worry about what that other formation is doing. You can attack without nearly so many worries - so long as you don't open the path for this formation to get out into the rest of the North, Lee has to withdraw back over the Potomac. It's a chance to do some damage and possibly conduct a concentric attack.
- If all of Lee's men are at Sharpsburg, same basic deal. Chance to do some damage.
I think this might be part of why it is that Lee moved on the 17th.