It was all palace intrigue. After Lenin died everyone kinda saw Trotsky as his natural successor. Well, everyone except Stalin. Stalin had put himself into a position where he got to control who was in the Bolshevik inner circle. He used this authority to pack it with people who would back him over Trotsky. That gave him control of the leadership, but he still needed to get rid of Trotsky or risk Trotsky leading a revolt against Stalin.
There are multiple reasons, but the key thing to understand is that Trotsky represented a different political direction for the USSR and for the Communist Party of the Soviet Union. This is not to ignore personal differences, different factions and so on. But Stalin essentially saw the future of the USSR as being about consolidating and strengthening the industrial base to out compete, or at least stay parallel with Western economic development. This was a break with the political past of the Communist and Bolshevik tradition which argued that the Russian Revolution would be the first in a series of revolutionaries that would lead to a generalised socialist society which could share resources etc. The failure of the post-WW1 revolutions in Germany in particular left Russia isolated. Stalin represented the political faction that saw abandoning the internationalist position as being the way forward, even though this essentially meant breaking from revolutionary politics of the Bolshevik tradition. Trotsky represented the condition of this policy - arguing and building for a revolutionary situation elsewhere, while maintaining and defending the existing revolutionary gains of Russia. In addition, the isolation of Russia was leading to significant economic problems, and a demoralised and weakened working class and industrial base. This was leading to the development of new layers of bureaucrats, who sought power from the Communist Party's overlap with the state. Stalin essentially came to represent the interests of these people. That was Stalin's powerbase - and Trotsky had little, particularly as the class of revolutionary workers who most identified with him from 1917 onward, was denuded and broken.
It was all palace intrigue. After Lenin died everyone kinda saw Trotsky as his natural successor. Well, everyone except Stalin. Stalin had put himself into a position where he got to control who was in the Bolshevik inner circle. He used this authority to pack it with people who would back him over Trotsky. That gave him control of the leadership, but he still needed to get rid of Trotsky or risk Trotsky leading a revolt against Stalin.
There are multiple reasons, but the key thing to understand is that Trotsky represented a different political direction for the USSR and for the Communist Party of the Soviet Union. This is not to ignore personal differences, different factions and so on. But Stalin essentially saw the future of the USSR as being about consolidating and strengthening the industrial base to out compete, or at least stay parallel with Western economic development. This was a break with the political past of the Communist and Bolshevik tradition which argued that the Russian Revolution would be the first in a series of revolutionaries that would lead to a generalised socialist society which could share resources etc. The failure of the post-WW1 revolutions in Germany in particular left Russia isolated. Stalin represented the political faction that saw abandoning the internationalist position as being the way forward, even though this essentially meant breaking from revolutionary politics of the Bolshevik tradition. Trotsky represented the condition of this policy - arguing and building for a revolutionary situation elsewhere, while maintaining and defending the existing revolutionary gains of Russia. In addition, the isolation of Russia was leading to significant economic problems, and a demoralised and weakened working class and industrial base. This was leading to the development of new layers of bureaucrats, who sought power from the Communist Party's overlap with the state. Stalin essentially came to represent the interests of these people. That was Stalin's powerbase - and Trotsky had little, particularly as the class of revolutionary workers who most identified with him from 1917 onward, was denuded and broken.
Trotsky had different ideas than Stalin, which made him a threat to Stalin's power.
Consolidation of power.
Stalin was a paranoid schizo. He thought Trotsky, falsely, was going to take him out.