Consider the following hypothetical:
Under New York law, your non-compete agreement is clearly unenforceable: it's overly broad in both duration and geographic scope, and your employer doesn't have any real legitimate interest that is deemed protectable, as articulated by New York's courts. So, you leave voluntarily (i.e., you quit your job), and immediately start working for a competitor across the street.
When your former employer tries to haul you into arbitration based upon your violation of the non-compete, you decide you would rather litigate the viability of the non-compete before New York's courts instead; after all, their law seems more favorably disposed towards your cause.
Seems rather straightforward, right?
Absolutely not - at least according to the highest court in the land. In its November 26 opinion in Nitro-Lift Technologies, LLC v. Howard, the Supreme Court specifically held that as long as the underlying agreement to arbitrate is valid, the Federal Arbitration Act specifically requires all issues regarding the enforceability of the non-compete clause to be decided by the arbitrator rather than the courts - even where the State's laws expressly prohibits enforcement of that particular type of non-compete agreement.