I've asked this to a few of the doctors at the first hospital and now here and received different answers. For the most part, there's no predicting how one gets leukemia. It's a mutation of the blood cells (or something like that), and happens randomly.
However, my first doctor, in response to my question "How did I get this?", answered, "Well, did you live near a refinery or nuclear power plant?" I hadn't of course.
And then I remembered taking this picture of my cat a few weeks before going to the hospital:
It's all starting to make sense...