Most homeowner liability claims come from everyday life: a pet, a guest's fall, a backyard fire that spreads, a child's mischief. Liability insurance exists to cover careless mistakes, not deliberate harm.
Dog bites: California Civil Code §3342 makes a dog owner liable to a person bitten in a public place or lawfully in a private place, including the owner's own property, regardless of the dog's former viciousness or the owner's knowledge of it. There is no first-bite defense, so an invited guest bitten by a gentle dog still has a claim.
Carelessness vs. intent: Ins. Code §533 relieves an insurer only of a loss caused by the insured's wilful act. The same section says the insurer is not exonerated by the insured's negligence. A homeowner who carelessly leaves lighter fluid by the fence is still covered when the fire spreads.
Children: Civil Code §1714.1 imputes a minor's wilful misconduct to the parents. Under §1714.1(e), an insurer is not liable for that imputed conduct beyond $10,000. The statute's separate cap on the parents' own liability (a $25,000 base, adjusted by the Judicial Council every two years) is not the insurer's cap, so parents can owe more than their insurer pays.