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Custer was defeated at the Battle of the Little Bighorn because he made a lot of fundamental errors.

1. He acted alone - even though Gibbon's last words to him were - Custer, don't be greedy. Wait for us.
2. Instead of going round the Wolf Mountains, Custer force-marched his men through the mountains. His troops and horses arrived tired after the long march.
3. He weakened his forces by dividing them into three - although this was classic US Army tactics.
4. He expected the Sioux warriors to scatter and run. Instead they outmanoeuvred and surrounded him.
5. He was hugely outnumbered.
6. He was arrogant and over-confident, and wanted the victory to bolster his political ambitions, he was considering running for President in future. He ignored the advice of his Crow scouts to wait for reinforcements.
7. The Sioux leaders - especially Crazy Horse - were expert and experienced generals.
8. The Native Americans regarded the war as their last chance - they fought with desperation.
9. The Sioux were determined - The whites want a war and we will give it to them, said Chief Sitting Bull.
10. Custer had poor information - he did not know how big the Sioux army was, nor that they were armed with Winchester repeating rifles.

Although Crazy Horse may have won the Battle of Little Bighorn, it was only a temporary halt to the advances of the Plains settlers and American army. If anything, it made them more determined to force the Native Americans onto smaller and smaller reservations.