If I offered you a 1 in 2 chance of winning $1 for 60 cents you'd probably say no. After all, the expected value is 50 cents so you're more likely to lose than win.
And yet, if I offered you a 1 in 2,000 chance of winning $1,000 for 60 cents, you might agree. The expected value is the same, but the payoff (even though far less likely) is much higher. If I offered you a 1 in 20,000 chance of winning $10,000, you might be even more like to give it a go "just in case" you win.
Lotteries and casinos rely on the fact that, even with big payoffs, things will average out in their favour.
Now consider insurance...
If there's a 1 in 2 chance an event might cost you $1, you're unlikely to take out insurance with a premium of 60 cents. However, if there's a 1 in 2,000 chance an event might cost you $1,000, you are more likely to be willing to be willing to pay a premium of 60 cents. Even if an event has only a 1 in 20,000 chance of happening, if it would cost you $10,000, you might consider paying a premium of 60 cents for insurance. If the 1 in 20,000 event would cost you $1,000,000 you might be willing to pay $60 or more in premium.
An insurance company (or even non-profit cooperative) is no going to offer you a premium less than the expected value. If there is a 1 in 20,000 chance they'll have to pay out $1,000,000 you're going to have to pay at least $50 in premiums.
The important point here is that insurance only makes sense if the likelihood of needing it is low. If the need is high, the premium will be close to the payout and, it's probably just not worth it. (Literally "probably" :-)
Insurance is about trading off an unlikely high cost for a definite low cost.
What about a situation where the event is almost certainly going to happen? In such a case, insurance is going to cost more than its worth. If it is known I'm going to have an event which will cost me $1,000, no insurance company is going to cover me for a premium less than $1,000.
And yet, people take out health insurance which covers highly probably or even certain events.
If your insurance covers an annual checkup, or new glasses every three years or a teeth clean every six months, or a regular therapy appointment: IT'S GOING TO COST MORE THAN IT'S WORTH.
In the case of predictable but not-that-frequent events, a case can definitely be made for trading off an infrequent (but likely) high cost for a frequent low cost. But this is NOT insurance. It's really just a type of amortization.
The fact that likely events get bundled in with real insurance is one of the reasons, I think, why health insurance is so expensive in the US.
POSTSCRIPT: A while ago I read about people in India who offer you insurance against the fine for riding on the train without a ticket. The cost of taking the insurance is less than the cost of the ticket, so morals aside, you're better off taking the insurance and not buying a ticket. Clearly this is a price signal that the ticket-to-fine ratio is higher than the chance of getting caught and either the ticket price should be lowered, the fine increased, or the chance of catching culprits be increased.