Because the Germans doing it seemed like such a good idea? Now the Allies opt for intervening in Russia.

And Woodrow Wilson decided that the U.S. would participate in it, over the objections of Army which advised against it.

Everything about Russia during World War One has a certain pipe dream quality to it.  The Western Allies had hoped from day one that the giant nation would prove to be a vital and decisive ally. It did turn out to be a handful for the Germans, who ultimately defeated it, but the German hopes for what they had defeated and their greed meant that the fruits of that victory were never realized. 

Following Russia's collapse into civil war the Allies hoped that the situation could be restored and a new republican government would rejoin the war, a hope that was folly at best.  Ultimately that hope lead to the decision to intervene in Russian affairs, putting the Allies into the extraordinary position of fielding expeditionary forces that would deploy direction into a civil war when, at that very time, the Allies were on the verge of loosing the war themselves on the Western Front.

Perhaps it is somewhat understandable, but only somewhat.  There was really no earthly way that Russia was coming back into World War One.  Moreover, the force needed to insure a quick White Victory, which is what would have been necessary to achieve that result, just wasn't there. . . which suggests that the Allies thought the Reds weren't really as powerful in 1918 as they were.  Not that they were not challenged, to be sure.  The Whites were also powerful at that time and the Communist government had seen an uprising on July 6 and 7 from the left, in the form of an attempted seizure of the government by the Left Socialist Revolutionaries.  Russia was a mess.

But the Allies, in the midst of the largest war since the Napoleonic Wars, weren't going to be able to reverse that.

Indeed, in the American Army's case, they weren't even going to be given a clear mission.