Seems like a straightforward question but I can't find a proper explanation because of how mythologised this war is.
Napoleon was a great military mind, he had a numerical advantage over Russians - at least at the beginning. We don't usually think of Kutuzov as one of the greatest generals of all time so it's not like Russians were genius. There's usual memetic explanation of General Winter but I prefer to think one of the greatest minds of the age knew that winter may be cold. Popular explanations in media (think War in Peace) say something about strength of Russian spirit and something wrapped in enigma but this is beside the point. From any point of view I can imagine Napoleon did something wrong.
I'm interesting not so much in reasons for French loss but in what decisions made by Napoleon were wrong.
Modified from an earlier answer of mine
The occupation of Moscow and the French retreat in the winter loom large in the cultural memory of the 1812 campaign to the point where they become a singular point of reference when talking about Napoleon's defeat. But as dramatic as the burning of Moscow and images of retreat through the snow are, this obscures the salient fact that Napoleon's campaign had gone off the rails quite a bit before he reached Moscow. When Napoleon met Alexander I's envoy General Alexsandr Balashev in 1 July in Vilnius, Napoleon fumed at the fact that he had occupied a whole province of Russia without so much as a major battle. "I'm already in Vilnius and I still don't know what we are fighting for," the Emperor is alleged to have said. Later in the interview, Napoleon ripped a window from its hinges and threw it into the courtyard below. Such frustration was understandable since many of the problems for the campaign was apparent at its start.
Urban centers like Moscow nor St. Petersburg were the primary targets of the French invasion. Napoleon's main goal when he crossed the Niemen River in June 1812 was not to occupy Russian cities, but to destroy the Russian armies as soon as possible. Napoleon pinned a lot of hopes on being able to pin down and crush the main Russian forces with overwhelming force. This was a problematic strategy for a number of reasons. For one, the Grande Armée was simply too large and unwieldy to use in a speedy fashion. Napoleon's own centralized command decision process, which had become a bit too rigid by this period, added to the problem. Micromanagement denuded the Grande Armée's corps some of their initiative so that when they were sluggish when they came into contact with Russian forces. Secondly, rivalries and hatreds among Napoleon's corps commanders made it very difficult for them to work as a team, and Napoleon's own confused staff work compounded matters. Napoleon's brother Jerome was ill-suited to his position as commander of the VII Corps and created no measure of headaches for French command. Third, the hot summer weather and terrain made it difficult to conduct speedy operations. The summer march ate into supplies and draft animals and contributed to outbreaks of dysentery and other ailments that wasted away the strength of the Grande Armée.
Finally, one has to give the Russians their due in thwarting Napoleon's plans. The Russian command was polarized between two camps on how to meet the French invasion. The defensive camp centered around War Minister Barclay de Tolly called for fighting a staged delaying action that would exhaust the enemy as it advanced into the interior, where it would be counterattacked by overwhelming force. A more aggressive strategy was championed by the likes of Prince Peter Bagration set the Oder as the final line of French advance and the the Russian army should immediately counterattack once the French invaded. Neither stratagem played out in 1812, but the command paralysis between these two camps encouraged a retreat towards Moscow. Retreat became the path of least resistance in the earlier half of the campaign even if it created grumblings among the "Russian" generals that "Germans" like de Tolly did not have the stomach to fight a foreign invader (sidenote: these ethnic categories were slippery in the Russian army with Bagration hailing from a Russified Georgian family and de Tolly from a Scots family that married into the Baltic German nobility).
The result was that the two armies that faced each other at Borodino were exhausted and rather less effective than they had been at the start of the campaign in June. Napoleon carried the day, but Grande Armée was in no shape to pursue the still large remnants of the Russian army. But Moscow appeared before Napoleon as a prize with no real force standing in his way to take it.
Herein lies a sometimes overlooked strategic myopia in Napoleon's grand strategy: he overestimated the importance of taking key cities to military operations. Napoleon sat in Moscow, which even after the fires there was a considerable amount of the city left, hoping that this would lead the Tsar to make terms. Moreover, his Bulletins back to France emphasized the importance of Moscow and the glory achieved in capturing it. The city's capture was one of the few bright spots in an otherwise dismal campaign that had achieved relatively little for its efforts and the gargantuan size of the army. But Napoleon did not possess the supplies to winter in the city and there still was an extremely sizable Russian army in the field. Moscow became something of a poisoned chalice for Napoleon; he placed great political stock in occupying it, but he could not keep it. Additionally, recent lessons should have shown him that occupation of a capital did not end wars. Neither the occupation of Madrid in 1808 nor that of Vienna in 1809 ended the wars there. In the following campaign in 1813, Napoleon developed an obsession with taking Berlin in the hopes of knocking Prussia out of the war, but this would not have been the shattering blow he anticipated. Russian forces had occupied Berlin during the Seven Years' War for four days in 1760 and almost again in 1762, and that did not cause Frederick II to abandon the war. If anything, the independent actions of the Prussian army chiefs in the winter of 1812/13 showed that they prioritized defeating the French far more than even loyalty to the Hohenzollern crown.
Such it was with the Russian army. The longer Napoleon occupied Moscow in the hopes for a political settlement that would not come, the greater sway the Bagration camp possessed over the more cautious "foreigners" like Barclay de Tolly. The result was that the Russian military became more aggressive even though it lacked the strength to challenge Napoleon directly. In the meantime, Russian forces blocked Napoleon's alternate escape routes via the Kaluga, so the Grande Armée had to retreat over its own line of advance, which had been twice picked over by the two armies in the summer.
The agonies of the retreat often serve to highlight the role of "General Winter" in Russia's defense but this distracts from another general that played an arguably bigger role in Russia's military history: General Distance. The sheer size and scale of Russia makes it very difficult to fight the type of campaign predicated on locating enemy forces and pinning them down. Even the mechanized armies of the Second World War had great difficulty in closing the gaps in the massive cauldron battles of the Eastern Front. These problems were doubly true for the Grande Armée of 1812 where an army large enough to deliver a knock-out blow to the Russian Army was too unwieldy of an instrument to actually land such a blow early in the campaign. Napoleon's command arrangements made matters worse, but the scale of the Russian interior would have probably stymied a more functional command structure.