Generalia Specialibus Non Derogant, meaning, the provisions of a general statute must yield to those of a special one. 
CALEA, in Section 103b1 of that act, the Feds gave up authority to require any specific design of equipment, facilities, services, features or system configurations from any phone manufacturer. 
The All Writs Act: “…may issue all writs necessary or appropriate in aid of their respective jurisdictions and agreeable to the usages and principles of law.”
The AWA is a general provision. CALEA section 103b1 is a special provision, which specifically states what the FBI and courts can’t compel Apple to do.
As Justice Brewers argues in Rogers v United States, 1902:
“The reason and philosophy of the rule is, that when the mind of the legislator has been turned to the details of a subject, and he has acted upon it, a subsequent statute in general terms or treating the subject in a general manner and not expressly contradicting the original act, shall not be considered as intended to affect the more particular or positive previous provisions, unless it is absolutely necessary to give the latter act such a construction, in order that its words shall have any meaning at all.“(Emphasis mine) 
That’s right. In order to prevent general provisions from forever barring specific provisions from having any meaning, specific provisions must take priority. There are a lot of general provisions in law, in particular in the Constitution.
As Magistrate Judge James Orenstein says, “In particular, unlike the government, Apple contends that a court order that accomplishes something Congress has considered but declined to adopt albeit without explicitly or implicitly prohibiting it is not agreeable to the usages and principles of law. Before discussing that matter, however, I first briefly consider how this case would come out if, instead of rejecting the government’s understanding of the AWA’s gap-filling function, I adopted it. Even under that reading of the law, I believe Apple has the better argument both because it is arguable that CALEA explicitly absolves a company like Apple of any responsibility to provide the assistance the government seeks here and also because even if CALEA does not have such an explicit prohibition, it is part of a larger legislative scheme that is so comprehensive as to imply a prohibition against imposing requirements on private entities such as Apple that the statute does not affirmatively prescribe.” 
Why might the FBI be pushing this so hard, when it is so clear the law does not allow it to make the request it has made?
The most interesting aspect to this case I found, is that the Executive (through the FBI, and under Barack Obama’s approval) have worked with a single court to try to undermine the specific powers limited to it by Congress. This is an excellent example of Checks and Balances. Congress worked with the Executive to craft a piece of Legislation that would Balance the needs of Law Enforcement with the Check against their power.
However, the FBI is saying that specific piece of Legislation is invalid as soon as a warrant is issued, and especially so once the All Writs Act is invoked.
What the FBI is saying, is that it can ignore the Legislative so long as the Judicial sides with it on this matter. Except, our Laws aren’t “Democratically” followed. Just because two branches want to ignore a third, doesn’t mean they just can, legally. They must present arguments and make cases, so that its publicly known under what circumstances and what precedent they are setting.
This is incredibly important. Otherwise, the FBI, with just a single lone, lowly court, can take a warrant (The “OK” from the Legislative) and the AWA to command any entity or organization or person to perform any task, even if it is in direct opposition to an explicit piece of Legislation.
Of course, the best argument for this is that the Judicial, and the Executive, must sometimes make decisions in extreme or imminently dangerous circumstances.
Except, it hasn’t made that case. It has only waved alarm bells. And if we really look at this specific case, the attacker destroyed his personal phone, which is quite telling: he knew important information was on that phone and needed to be destroyed. But not the work phone.
Likewise, under PRISM and other dark programs from the Executive, it should be clear whether that number contacted anyone of interest. The argument? Well maybe he talked to people we don’t know.
In other words, the Executive has no reasonable belief the information on that phone may prevent an attack, it has only circumstantial belief.
Even if the argument is that we must stop terrorists, why is it that a single terrorist attack, which was highly localized and with minimal damage to the country, allow us to completely overrule our basic laws and liberties? Why not other forms of crime?
Why even have limitations on the Executive at all, if every attack and every crime is “special”, and warranting super-powers be granted to the Executive for any case, no matter how unclear the case may be in terms of damage, no matter how unclear the FBI’s methods were used to determine its authority in the matter, no matter how unclear it may be of the reality of the world?
The reason the FBI is pushing this case is obvious. And I said it before. This has nothing to do with terrorism or encryption. This is all about the FBI wanting to expand its powers and explicitly bypass CALEA, Legislation passed and worked on by the Executive and Legislative, in a manner wholly authoritarian for reasons out of fear. The FBI wants unlimited powers to exploit through a single corrupted Court judge.
Even if another attack were to happen, and it “could have been prevented if we had the information on that phone”, does not validate the government’s position to supercede law. If it’s so important, new provisions should be made, or an actual declaration of war or Emergency Powers granted by Congress. There are so many tools for bypassing law that are established and known, with a clear purpose and extraordinary understanding, with a clear time-limited position.
This isn’t a conspiracy. This is exactly what the FBI is doing, and its blatant and its clear.
The FBI cannot be allowed to win this case in the manner it is doing. Not because the FBI shouldn’t be allowed access to that phone (ethically, utilitarian, whatever argument you want is valid). But legally speaking, it cannot be allowed to win in the manner it is pursuing.
This is an incredibly important distinction not being made by the Media. It is being portrayed as Ethics against Law, when its really Ethics against the Philosophy of Procedural Law. I cannot highlight enough how incredibly important this distinction is.