Earlier quoted context omitted.
A simpler way of explaining it is that both activities have a negative expected value but insurance usually reduces variance while gambling increases it. In the context of money variance is usually synonymous with instability and unpredictability. Those things are bad and it’s worth paying a fairly priced premium to avoid them. In simple math terms gambling is essentially the opposite dynamic. Of course things that a…
Variance can be good though. Imagine you want some expensive service like a waterline for your house that's difficult to steal but you live under rules of gangsters or oppressive government so holding anything more than a little money at a time is risky. You gamble every paycheck knowing eventually you will get a big payout. You quickly pay for the waterline and now you don't have to walk 300 ft to the well everyday.
That's why I mentioned that "avoiding variance" in itself is not a good argument. You avoid it for a reason and that reason is that (u(x - a) + (u + a)) / 2 < u(x) for vast majority of life scenarios.