Oh, there's no question that sometimes you'll be better off with the insurance. It's just that most of the time you won't be.
When I say negative expected value, I mean something like a gamble with an 80% chance of losing $50 and a 20% chance of winning $100. It's certainly possible you'll come out ahead, but the odds are you won't. (The expected value of this gamble is -$20).
Homeowner's insurance insurance is something like (I'm totally making this up) each year taking a gamble with a 99.99% chance of losing $700 and a 0.01% chance of AVOIDING LOSING $300,000 dollars. You do it anyway because even though the gamble has a negative expected value (-$670) you don't have $300,000 to replace your home and possessions: you do it to avoid the risk of catastrophic loss.
Buying insurance can also bring peace of mind, which may be worth the extra money as well.
So there are several things to think about, including what would happen if you got unexpectedly hit with a vet bill of several thousand dollars and how much the peace of mind is worth to you. However, don't go into it expecting to save money with the insurance. There's a chance you will but it's more likely you won't (if that weren't true, the insurance company would lose all its money and go out of business!)