Why did Napoleon divide his army during the retreat from Smolensk?

Organization of disorganization

First of all, we must note that armies in general tend not to travel in one enormous body of men, horses, vehicles etc ... This was true in Napoleonic times as it is today. Reasons vary from operational and tactical, to logistical. Army needs advance guard, it needs rearguard, patrols covering sides of the road. It also needs night quarters, especially in dreaded Russian late autumn/winter. It also needs food and forage, and this tend to be in villages around the road. If units in the army march some distance form each other, they could use same houses for the rest. If not, someone would need to stay at the side of the road. Beside all of this, units tend to travel in different speeds, therefore it is somewhat natural they would spread around the road.

Now, considering Grande Armée specifically, things were not good even when they left Moscow on 19th of October 1812. Day before that part of the army was defeated at Tarutino. Actual number of men under flag has declined from around half million at the beginning of campaign to near 100 000, due to illness, losses and desertion. For the average French soldier (actually, there were many foreigners in Grande Armée) capture of Moscow was peak of the war. They were promised this by their superiors, and when they got to the city concerned themselves mostly with looting valuable trinkets instead of gathering food and clothing for a winter campaign. At the battle of Maloyaroslavets French still had certain control of the troops (i.e. they would rally around the flag) , but that would soon deteriorate and there would be lots of stragglers just moving in general direction of the army, at their own pace and not belonging to an organized unit.

Anyway, Napoleon decided to go to Smolensk using old beaten path, again across Borodino, not trying to force his way to Kaluga. Interestingly enough, Kutuzov was at first ready to block his way to Kaluga, but latter changed his mind, so actually both armies retreated from Maloyaroslavets. There is old what-if scenario about what would have happened had Napoleon retreated trough Kaluga. IMHO, nothing particularly important. Reason for that is that already after Maloyaroslavets, Grande Armée started disintegrating. One example of this was Battle of Vyazma that happened on 3rd of November 1812, some ten days after Maloyaroslavets. French army has already stretched out to 100 km and as a result Russians found gaps between main body and rearguard, infiltrated the road and inflicted heavy casualties .

As a result of this, French were even more stretched out when they started arriving in Smolensk around November 9th 1812. Again, tail of the column was dragging for miles behind the head. Conventional wisdom would dictate that Napoleon rest, resupply and concentrate his forces, possibly even prepare for the battle against incoming Russians. Instead, troops arriving into Smolensk started looting supplies that could have saved them, and discipline could not be restored even in Old Guard. It looks like that from that moment French soldiers were willing to fight only to get out from Russia, i.e. they would follow the orders only if those orders were in line with their wishes to retreat westwards.

Napoleon was faced with simple choice : either to wait in Smolensk with more and more arriving troops turning into a mob and looters, or to dispatch piecemeal those that had their share of the loot westwards, where they wanted to go anyway. Since he considered Russian army to be further away than they really were, he decided for the latter action. Theoretically , this would allow rearguard troops to at least have some rest if not resupply in previously occupied quarters. Unfortunately for them, Russians were closer then expected and again caught units at the rear in Battle of Krasnoi. Note that throughout this latter part of the campaign Kutuzov actually held back his commanders from unnecessarily attacking main body of the French army, focusing instead on disorganized and stragglers. One of explanations was that he sensed that the French would fight bitterly to escape, which historically they did even at Berezina. Therefore, it would be better to let them be softened or even destroyed by elements before attacking.

Final assessment of Napoleon's decision at Smolensk would be that it was forced decision. He no longer had an army that would obey his commands unquestionably. Instead, this was a mass of men with some military reflexes and learned behavior, but also mostly motivated with survival instinct of every man for himself. As long as others among them worked towards common goal (escape from Russia) they would cooperate with them. If not, they would simply cast of military discipline and strike on their own. By retreating piecemeal, he at least could have hopped that vanguard of his army could save themselves.