What did Dostoevsky mean by this quote…
“…socialism is not merely the labor question, it is before all things the atheistic question, the question of the form taken by atheism today, the question of the tower of Babel built without God, not to mount to Heaven from earth but to set up Heaven on earth.”*
In the Old Covenant (Old Testament) time, God’s salvation system was through the temple and Jerusalem. A temple is a stairway and a gateway to Heaven. The city around the temple is the cultural bed in which the temple rests. Babel, then, was a counterfeit Jerusalem and temple — an Old Covenant counterfeit.
In the New Covenant we see, not us going up to Heaven, but rather, Heaven coming down to the earth (Revelation 21). What then would a New Covenant counterfeit look like?
Dostoevsky recognized socialism as this counterfeit.
* Dostoevsky, Fydor, The Brothers Karamazov (Barnes & Noble: New York, 2004 [1879-1880]), pg. 32.
Pursuit of Percipience 
“Socialism is a philosophy of failure, the creed of ignorance, and the gospel of envy, its inherent virtue is the equal sharing of misery.”
–Winston Churchill