I don't know how people came to think that "the banality of evil" means "evil people are people too". It's also true but it's not what the banality of evil means.
The term was coined by Hannah Arednt in her report on the trial of Adolf Eichmann, the architect of the "final solution" in the Holocaust.
It describes the way in which the Nazis at large and Eichmann in particular have turned the horrendous act of mass murder into just another job, disconnecting themselves morally and emotionally from their actions.
Before the death camps and gas chambers, Nazi soldiers simply shot Jews into mass graves by the hundreds of thousands. It was a lot cheaper and faster, but it caused great psychological disturbance for the murderers.
Their solution was a massively upscaled version of the "gas vans" they used to mass murder hundreds of thousands Germans with disabilities and mental health issues.
Shooting bound civilians in point blank rank over and over is something you can't just pretend you're not doing or is no big deal. But if you're just the guy who sorts people into groups. Or just the guy that funnels them into a room. Or just the guy who opens a cannister on the roof. It's must easier to distance yourself from what you know is happening.
The same principle applies to much lesser evils, like soldiers operating drones from a distance, or insurance workers denying coverage for life-saving treatment.