Why do insurance premiums vary so much between companies?

Factual Questions
1

I was shopping for car insurance recently, and I’m surprised at how much the quotes differed between one company and the next. I have a few factors working against me, so they were all relatively steep; but for example, I saved about $3000 a year by choosing MetLife over Geico.

Now, I always thought insurance premiums were mostly determined by the amount you’re likely to cost the company in claims. But for the same driver, same car, and same policy, why would one company charge twice as much as another? Don’t they all use basically the same statistics?

Does one company really think I’m twice as much of a risk as the other does, or are they just trying to discourage people who fit my profile from signing up with them?

2

[1] Different companies provide different levels of personal service. A company that lets you talk to a human when you call will have to charge you more to pay for that service.

[2] Some companies just plain don’t want to sell certain types of insurance. For marketing purposes they have to have a complete set of products available, because the agents like it that way, but they raise the price to discourage people from actually buying the product. Perhaps Geico saves costs by discouraging people who “have a few factors against” them from buying their product.