I don't think it's betting against yourself. It's just allocating some funds to an alternative version of yourself that has had bad fortune. You can think of it probabilistically.
That's why it's usually not legal to take insurance out on things that are not you or that you own or are responsible for. Like me taking life insurance out on you, then convincing you to take up crack or simply killing you. I'm betting you're going to die at some odds, then I'm massively changing the odds in my favour relative to the initial bet. Insurance is just gambling with vast sums. Sometimes it makes sense, sometimes it doesn't.
No, insurance is gambling with small sums from the point of view of people selling it, and it is avoiding gambling with large sums from the point of view of people buying it.
But probabilistically doesn't it make sense to skip insurance altogether?
If insurance manages to turn a profit despite having overhead expenses (salespeople, infrastructure, lawyers, etc) and assuming they don't have a special discount in whatever they're ensuring then there are more people paying without using than there are people who need it.
If I'm an average or above average driver, for example, then it doesn't make sense to have insurance, does it? Wouldn't it make more sense to save the money I'd otherwise be using for insurance and pay myself in case something happens? That way my money would go only towards my problem and not towards worse drivers and insurance company expenses.
Is the product that insurance offer really just peace of mind?
You’re waiting at a red light when a drunk driver smashes into you. Your skills as a driver can’t affect the probability of this. It may not be your fault, but someone needs insurance.
The difference between owning a total of 0 and a total of 10000 USD is way more important than the difference between owning 10000 and 20000 USD.
So assume you have 20000 USD. There's a 10% change that you will lose it all and become homeless. It makes sense for you to pay 2000 USD at the start to get 10000 USD back in case that happens. Because being homeless in 10% of the cases is way worse than having 18000 USD instead of 20000 USD in 90% of the cases.