Why did they start in New York? In order to do business in New York, an insurance company has to be headquartered (incorporated) there. (Edit: No other state requires this.) And New York is expensive.
They probably started in NY because most of the founding team is living in/near NYC, according to a document filed with the NY DFS (http://www.dfs.ny.gov/insurance/exam_rpt/x9475o13.pdf). It also states that
"The Company is a wholly-owned subsidiary of Mulberry Health Inc. (“Mulberry”), a Delaware Corporation."
Perhaps they thought that the administrative costs stemming from operating in NY wouldn't make/break the company - it's whether they can substantially reduce the claims costs that will really determine the outcome. And if they're from NYC, the founding team probably had preexisting contacts in the local medical institutions, which made it easier to form the partnerships that are key to making Oscar's business model work. One of the founders is Joshua Kushner (https://en.wikipedia.org/wiki/Joshua_Kushner), whose family is well-connected in NYC (for example, his brother's father-in-law is Donald Trump).
The insurance giant I once worked for also has a wholly-owned subsidiary in New York. This is probably a common tactic for coping with the ...quirky New York law concerning "No insurance company can sell insurance in our state unless you incorporate in our state."
I know something about the history of the insurance giant I worked for. I know that their success has a lot to do with one of the founders having been a lawyer by trade and making strategic choices concerning things like where to found their headquarters.
I have trouble fathoming doing something less strategic while hoping to break into such a highly regulated industry, basically.
This sounds dumb to me.