Custer was an arrogant ass. He left his "machineguns" and a third of his troops behind when he road into Big Horn.
Ironically, taking the Gatling Guns along (as General Terry had offered) might have saved Custer --- just not in the way it might be thought. They would have slowed his column down as they were cumbersome, often causing problems. Had Custer brought them, they would have been of limited use in the broken terrain, laced with coulees and hills that would have provided cover and concealment for the advancing Indian warriors, but no protection for the cavalry against the Sioux arrows, which are not necessarily line-of-sight weapons.
The delay bringing the Gatlings along would have allowed the Terry/Gibbon column, which made its own serious blunders approaching the Indian encampment, delaying them about 24 or more hours, time to catch up, and possibly an opportunity to join up with Custer's 7th.
He didn't "leave a third of his troops behind" when he road into battle, he separated them into two columns, one under Major Reno, the other under Captain Benteen. Reno's column hit the village first, but Reno failed to hold the momentum, panicked, and fled back across the Little Bighorn River, met up with Benteen, who decided not to join Custer but take up on what became Reno Hill and hold a purely defensive position with the inexperienced dingbat Reno.
Was Custer arrogant? Hell ya, but in the army of his day he did not have the ego market cornered; he was a bit player. He was a limited soldier with more luck than strategic expertise, and he paid the price, along with a couple relatives and a few hundred men on a terribly hot day on a hill near a infamous river.