1) Little Bighorn.
2) The battle (massacre) of Washita.
3) Leading an expedition to open up the Badlands.
Most people don't know about 3), or don't consider it remarkable, so they focus on 1) and 2).
One could argue that Custer's intent at Little Bighorn was a sneak attack that would turn into a rout if not a massacre. In other words, he was acting as an "Indian killer" even if his plan utterly failed. Hating him for that is somewhat understandable. It's like hating Hitler or Stalin for being anti-American even though they never attacked the US.
But really, Custer's infamy among Indians is mostly due to Washita. Along with Wounded Knee and Sand Creek, Washita was one of the "top three" massacres in the Indian Wars. There may have been one or two others where more Indians died, but these are the ones we remember.
Other "Indian fighters" may have killed more Indians over time, but Custer a) killed dozens in one swoop, and b) knew how to attract and hold the public's attention. I suspect Washita cemented his fame as an Indian fighter--with Custer stoking the legend himself.
Custer the symbol
When people like me list Custer as an Indian hater or killer, it's really because most people know him as one. He's useful as a symbol of anti-Indian aggression, not because he was a racist who hated Indians. Because of Washita and Little Bighorn, he represents someone who wanted to kill Indians, even if he didn't do that much of it.
In fact, Custer's view of Indians may have been typical of the times: he admired their fierce fighting prowess, but thought they had to get out of the way of progress. At one point he even testified on their behalf:
Custer open to interpretation
So I'm not sure any firm conclusion about Custer is possible. He led one of the worst massacres of Indians, but otherwise he didn't do much against them. Does that make him much worse than average, just average, or what? Depends how you rank the moral crimes, I'd say.
A better choice for Indian killer would be Col. John Chivington, who led the massacre at Sand Creek. I believe he genuinely hated Indians and thought they should die. Most Indian fighters respected their foes, but not Chivington.
I guess your friend could be a fan of Custer's Civil War record, or his larger-than-life personality. It would be like admiring the South's generals even though they lost the Civil War. But if he's a fan of Custer's Indian record, I'd have to ask why. Unless you think hunting and killing Indians is good, Custer didn't do anything great in the post-war years.
For more on the subject, see Racist Pro-Custer Website and Why We Love Custer and Indians.