Discuss three reasons why Russia withdrew from the First World War?

1). The Bolsheviks came to power. One of the biggest mistakes of the Provisional Government that took power in the February Revolution of 1917 was that it continued Russia's involvement in a war that was widely unpopular. Russia had sustained enormous losses during World War One without much in the way of territorial gain.
When the Tsar was overthrown, many Russians believed that the country would pull out of the war. That this didn't happen played into the hands of the Bolsheviks, who'd been opposed to the war from the start, seeing it as nothing more than a quarrel between the crowned heads of Europe that had nothing to do with the working classes.
After the Bolsheviks took power in October 1917, they immediately set to work disengaging Russia from the war, eventually signing the Treaty of Brest-Litovsk, which ceded vast territory to Germany in return for Russia withdrawing from the conflict.
2). The war was deeply unpopular. As we have seen, Russia didn't seem to get much out of its involvement in the war. More than most of the participants, Russia was greatly impoverished by the conflict, enduring chronic shortages on the home front for very little strategic gain. The Bolsheviks skillfully exploited the war's unpopularity, and by making themselves the most consistently anti-war party, they put themselves in a prime position to stage an armed insurrection against the Provisional Government.
3). The fall of the Romanovs. The fall of the Russian royal family, after more than 300 years on the throne, spelled the end of Russia's involvement in the war. This did not happen immediately, of course; as we've seen, the Provisional Government made the huge mistake of keeping Russia in the war. But without the autocratic system of Tsarist government in place, it was inevitable that Russia would withdraw from the war at some point.
Initial Russian involvement in World War One was based on a sense of cultural solidarity with the Serbians, who were fellow ethnic Slavs. The Tsar, like all his predecessors, saw himself as the protector of fellow Slavs, wherever they were, so Tsarist Russia didn't hesitate to join the war when it broke out.
However, once the Tsar had been deposed, that imperative no longer held. The Provisional Government had neither the inclination nor the ability to take up the mantle of pan-Slavism, so the original reason for Russia's involvement in the war was no longer valid. That the Provisional Government was unable to supply a compelling alternative justification was its undoing.