The White Russian counter-revolution was initially led by former Imperial commanders, and of course the fighting was begun by the Czech Legion in Siberia. Some White commanders wanted a democratic government; some wanted socialism but not the Bolsheviks; some wanted a government that was what we today would call fascist; and some wanted the monarchy restored.
Others wanted to set up as their own countries, or take over Russia with themselves as the new leaders. Still others simply wanted their own regional or ethnic groups to be totally independent. Their different political views, however, mattered less than the fact that they were widely scattered across the vast expanse of Russia, and had they wanted to cooperate they could not have.
The Bolsheviks easily put down the Right Social Revolutionaries, the Kadets and other such groups, but large armed forces in the Ukraine, the Kuban, and Siberia were far more difficult. General M. V. Alekseev in the Don region commanded the best anti-Red forces. Armies of Cossacks took arms against the Reds, and joined Alekseev, but their leaders were mostly clan leaders with no broad programs at all. The Finns and the Baltic states all threw off Russian rule during the upheavals, and managed to keep their freedom during the Civil War, but they were only interested in their national independence, not in sweeping idealogical aims. Admiral Kolchak set up a right-wing government in Siberia. General Iudenich attacked Petrograd from Estonia, but none of these regimes by themselves were strong enough to defeat the Red Army. Neither were the anarchist and regional ethnic militaries which rebelled against the Reds throughout the Caucases and the southern borders of Russia. None of these groups agreed on any kind of political program.
General Denikan, Alekseev's sucessor, with a force of White Russians and Cossacks reached Orel, some 250 miled from Moscow. His sucessor, Baron Wrangel, did best of all, consolidating power in the Crimea, but he was also eventually crushed by Trotsky's Red Army. Japanese, British and American troops held Archangel, Vladivostok and Murmansk for a time, until withdrawing in 1919. Allied forces also kept the Reds from seizing Poland. But Allied intervention and their support of the White forces alienated the population from the Whites, and the fact is that Lenin, Trotsky and the rest of the Bolshevik government were too adept at propaganda for the White forces. The Whites had a half dozen ideologies, and their forces were seperated sometimes by thousands of miles. The counter-revolution was doomed from the start.
The Whites weren't sure they all agreed on who would be the best leader. There were different levels of money. Some Whites also wanted more power than what they had before, which made them fight less for the current system that was under attack.