We are looking at this from different points of view.
You define predictable as: I can predict if and when this will happen to me.
I define predictable as: I can predict that this will happen one in one hundred times.
Both are correct definitions of predictability. In the insurance context, your view is the one of the insured and mine is the one of the insurer. The switch between the two occurs at some risk-adjusted monetary threshold. In other words, whether you are an insuree or an insurer depends on your risk tolerance. For example, most home owners are insurees for the purposes of fire. Most home owners are also (self-)insurers for the purposes of, say, a leaky faucet. The decision to procure insurance is therefore not predicated on the unpredictability of the event but on a risk adjusted monetary basis (ie, cash flow and risk hedging).
I'm using the standard dictionary definition of "able to be known, seen or declared in advance" (there's also "behaving in a way that is expected" which is not relevant). We are discussing events that are not known in advance, so by the dictionary definition, they are not predictable. Knowing the probability is not the same as you will not be able to say "it's going to happen this time".
Sorry, but you're using a bizarre definition of predictability. If I were to say that the chances of anything coming from Mars are a million to one, then you'd be considering it "predictable".
You define predictable as: I can predict if and when this will happen to me.
I define predictable as: I can predict that this will happen one in one hundred times.
Both are correct definitions of predictability. In the insurance context, your view is the one of the insured and mine is the one of the insurer. The switch between the two occurs at some risk-adjusted monetary threshold. In other words, whether you are an insuree or an insurer depends on your risk tolerance. For example, most home owners are insurees for the purposes of fire. Most home owners are also (self-)insurers for the purposes of, say, a leaky faucet. The decision to procure insurance is therefore not predicated on the unpredictability of the event but on a risk adjusted monetary basis (ie, cash flow and risk hedging).