Actually, Custer was known as an arrogant pompous a$$ among the Union officer corp. There was an incident at Appomattox, a day or two before the surrender, while negotiations were going on as to how to organize it, when Custer stormed up to the confederate picket and demanded to be taken to Lee and get his surrender. He threw a real conniption and provided entertainment for both sides. They sent him out west after the war just to get rid of him. His ego made him not follow the game plan and stay within a the proscribed distance of another group of soldiers and supply, and that is why he got his sorry self stuck at Little Big Horn and caused all the deaths of himself and men.
On the nose... Hence not too many statues of him around. and It would be stupid to have one at the Little Big Horn.