Although Trotsky was seen as the superior replacement for Lenin, he lost the leadership challenge due to a host of reasons. Even though Trotsky possessed such great leadership qualities he was one to make enemies quite easily. Leon Trotsky could easily be viewed as being arrogant, or also looking down on others that he didn't view to be as intellectual. He also had the habit of being naive, and also thinking himself to superior to the people he was surrounded by. He was also vain and ruthless. He enjoyed the higher qualities of life with good food and wine. But one thing which did make him no so much liked was the fact that he was Jewish. These qualities were not the best to possess if you were aiming to win the leadership challenge. Trotsky underestimated Stalin. Trotsky's weaknesses lead directly to his own downfall and his underestimation of Stalin is also a key part of Trotsky's arrogant nature.
Trotsky was not scared to speak his mind and his overconfidence lead him to assert his point of view even if all other members didn't agree, this created an image of the most likely person to cause a split in the party. A view magnified by the fact that Trotsky only joined the party in August 1917 after defecting from the Mensheviks. Due to his very strong views that he refused to back down from he was seen as the most likely to try and establish a dictatorship.
When Lenin had died many people had expected Trotsky to take over as he was closer to Lenin than anyone in the party was. But Trotsky had a few things against him which would eventually cost him his life in 1939.
One of the first things was that Trotsky was always on...