Absolutely not. In fact he was Commissar of War during the Russian Civil War. He organized it into an efficient military force and used it to defeat the opposition forces in the Civil War. Far from hating militarism, Trotsky believed in its use in order to preserve what was gained by the revolutions.
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Leon Trotsky built the Red Army into an efficient military organization.
Leon Trotsky was the first leader of the Red Army. He joined the Bolsheviks before and soon after became one of their leaders.
Autocratic
Leon Trotsky accused Joseph Stalin of being a tyrant and demanded democracy. Although Lenin wanted Trotsky to assume leadership after his death, Stalin's supporters out-maneuvered Trotsky. Stalin suppressed Lenin's will and manipulated Trotsky out of his post of Commissioner of War as well as out of the Politburo.
Joseph Stalin opposed Trotsky in their struggle for power after Vladimir Lenin died in 1924.