The approach I prefer is to answer with the truth, in as much detail as will make sense for the child, and as much as I myself understand. But when you reach the point that you don't know the answer, or don't know how to put it in a way that makes sense to the child, be honest about that too; saying "I don't know why they did it" is a perfectly reasonable answer.
My children are only a bit younger than your cousin (5 and 7) and ask some tough questions as well, including about the holocaust. I've told them what happened, though not in detail yet (as they haven't asked), and when they asked "why" I simply said, "There are some bad people in the world, and bad people sometimes are able to convince regular people to do bad things."
I also told them that there were lots of good people, too, in Germany as there are everywhere; the countless stories of Germans helping to hide Jews and others from the authorities, even sometimes at the cost of their own lives. (This discussion happened when we were on the plane going to Germany, to visit a family member stationed there, so it seemed particularly important!)
A child, especially a younger child, tends to see the world in black and white, and this will make things like the Holocaust seem impossible to understand to them. Remembering this may help in those discussions, because adding in the shades of gray is helpful - but also hard for them to understand, that the far majority of people are neither evil nor good, but somewhere in between.
One other thing to consider is to frame the answers in ways that help the children think more. Whys about atrocities like the Holocaust can lead to thoughtful conversation about not staying silent in the face of wrong; while we can hope the child will never be faced with that level of difficulty in their life, they may well see other children being bullied or mistreated, and it's something to think about as a parallel: do you speak up for those who have no voice?
There's also several resources on the internet for answering any given hard question. One tip from this Huffington Post article on young children asking hard questions applies to your cousin as well, I think; answer what is asked, but don't expand beyond it. It's easy to read more into the question (because you know so much more) than what is being asked.
For the Holocaust specifically, of course, there are a lot of resources. This article has a take I like.