The problem arises when there is a claim for a dog bite and the insurance company finds out the homeowners lied on the application. At that point, the insurance company can deny coverage and will most likely cancel the policy asap. The homeowner is then left to pay for damages all on their own.
That's the thing, though. Most owners of those breeds would likely be willing to sign an exclusion from coverage for dog bites, but when they ask for this, are flatly refused. So you can get the same result by simply saying no to those questions.
