"What's the law you're abiding with that says you need to implement such a backdoor? Name it. Even the FBI named the law or laws it thought would help it force Apple to put a backdoor in its phones."

A court order to enable warrantless wiretapping per FISA provisions. That's what they were doing with others per the leaks. The Sentry Eagle leaks, highest classification they had, indicated the FBI "compelled" domestic firms to "SIGINT-enable" their stuff with FISA mentioned repeatedly. It didn't define the methods they used to compel companies.

So, they have some way of leaning on them with the Patriot and FISA Acts as legal support. It shouldn't surprise you given it's happening in an active, police state with apathetic citizens who haven't forced Congress to roll back the legislation. Media has been fairly complicit, too, as they're not pushing the angles that would stir people into action. They watered down the previous debates.

Until these legislations are killed, there's secret courts, secret consequences, and gag orders that all these companies are faced with. Unlikely anybody will help them if they violate the rules that serve the state. So, it's on the citizenry to modify those rules so there's accountability. They mostly don't care. So, compliance with the court orders is rational choice by a company with no rational alternatives unless it intends to shutdown and make everyone jobless. Which will likely just shift business to competitors that secretly cooperate with the State. Like with Lavabit.

Note: Apple got to be lucky exception since FBI publicized the case and tried to fight in court of public opinion on top of an actual court. Terrible thing is we still don't know if they backdoored stuff for them with that being a show. Especially that HSM. It's illegal to know in the U.S..