This is, to some extent, an open research question which historians of that era's Middle East debate. Here are a few points which at least suggest an answer:

​

1-- Although it lost, the Ottoman military actually performed fairly well against strong enemies. Mustafa Kemal, who led the Turkish military through the war of independence, played a major role in the Ottomans' crushing victory over the British and Commonwealth expeditionary force which landed at Gallipoli. Ottoman forces also inflicted humiliating defeats and costly setbacks on the expeditionary force from British India which invaded Mesopotamia, and managed to stymie British efforts to invade Palestine from the Sinai at the same time. In the Caucasus and Eastern Anatolia, the Ottomans managed to limit Russia's gains until the Bolshevik Revolution knocked the Great Bear out of the war. That army's core, mostly made up of Anatolian peasants, continued to fight for Turkey during the War of Independence. (For details, see Leila Fawaz's A Land of Aching Hearts, a comprehensive history of the First World War in the Middle East)

​

2-- Britain and France were war-weary and faced a number of problems in both their longstanding colonies and the new mandates they had taken on during the war. France faced some especially major issues in their Middle Eastern territories in Syria and Lebanon, where the Hashemite prince Faisal's army, fresh off its victories in the Arab Revolt, tried to establish a united Arab kingdom with a capital at Damascus in 1920; other local notables and former Ottoman military officers led revolts against the French in Aleppo and the Alawite-majority mountains of Syria's west coast. Former Ottoman military officers also led a revolt in British-occupied 'Iraq in 1920. Many of the rebels in both countries were sympathetic to both the old Ottoman order and Mustafa Kemal's reformed Turkish Army. (For more info, see James Gelvin's Divided Loyalties, about Arab nationalism and Faisal's revolt, and Michael Provence's The Last Ottoman Generation, which is about how the Mandate period reflected the Middle East's Ottoman past and shaped its future trajectory.) The great powers' pre-war colonies also saw a great deal of unrest. Nationalists in India, Vietnam, and Egypt seized on Wilson's 14 points, which newswire services and American propagandists had spread throughout the world to argue for their own independence. (See Erez Manela's The Wilsonian Moment for more details.) Britain and France had little interest in sinking more resources into a conflict with Turkey which probably wouldn't bring them any more territory or resources; their Arab allies were mostly disillusioned or focused on local concerns (in the Hashemites' case, trying to stave off Saudi expansion). In general, Mustafa Kemal's army faced fewer and less determined enemy soldiers than the Great War-era Ottoman army had.

​

3-- The Red Crescent funneled donations and supplies from Muslims around the world (including residents of British and French colonies) to the Turkish army. Mustafa Kemal kept the final Ottoman Sultan on as a Caliph with no temporal power to encourage donations and a sense of Islamic solidarity with the Turkish cause (and got rid of him after the conflict was over.) Shipping lanes and lines of communication were more open than they had been during the First World War (when the British blockaded the Ottoman Empire), which made these transfers possible. (A lot of the major research about this point hasn't been published yet; I know about it because I saw a colleague present on it at the Middle Eastern Studies Association this past autumn.)