The white army failed to overthrow the reds, the Bolsheviks who had taken power in Ocober 1917, because of the following factors: they had no one leader, let alone an inspirational leader. The Bolshevik had Lenin.
They did not have a well organised and equipped army, nor were their soldiers wholly committed to a cause, so there were many defectors. The Bolshevik were manned and supported by a populous whose desires for the basic means of survival were at the very core of their party's ideology.
Finally, Lenin had within weeks of taking power, established a secret police whose role was to out any whisper of insurrection or espionage, and to counter it - usually viciously.
The White Army failed to overthrow the Bolsheviks mainly because the Bolsheviks received support from the working class of central Asia. While the Bolsheviks had Lenin as their leader, no one person was in charge of the White Army.
The Whites had several leaders – Yudenich, Deniken, Wrangel and Kolchak. All of them wanted glory for themselves; they fought differently without co-operation which made it easier for the Bolsheviks to defeat them individually.
Also, the Bolsheviks were fighting for a definite cause (the establishment and survival of a communist Russia) but the Whites had problems motivating their troops and building up support. Some Russians feared that foreign intervention might bring an end to Russian independence in the case of White victory.
Over time, many soldiers deserted the White Army; it wasn’t surprising to see the Bolshevik support increase dramatically given the choice between them and the Whites.