US health insurance companies are highly regulated, and that includes regulation that caps how much of customers' payments they're allowed to keep (the "medical loss ratio"). If they don't pay out enough for medical care, they have to return the extra money. They're incentivized to deny claims for the same reason any business is incentivized to reduce quality in order to cut price - because most people want a product that costs less up front.

(I think of myself as a relatively healthy guy, so whenever I have been offered a selection of insurance plans, I have always chosen the cheapest one without looking up denial rates. Maybe this isn't rational but it is common.)