Apple does not have a responsibility to help the FBI gain backdoor access to iPhones. By doing so, the FBI is given the ability to invade the privacy of millions of Americans at a whim. Cell phones have already become a hot button issue under the fourth amendment particularly in regards to whether a police officer can search through a cell phone during a traffic stop or arrest without a warrant. This would be an extension of that possible breach of citizens' fourth amendment rights.
If the FBI is allowed access to one phone, the FBI will want access to every one's phone so they can have access to all of the citizens private and personal property. With the FBI gaining access, means that every other person around the world has the same ability to gain access as well, even if they are not supposed to. Hacking may become more likely with a backdoor to our private information
The FBI accessing this iPhone would be a step in the wrong direction, but it's not the slippery slope leading off a cliff that Apple seems to think it would be. I support Apple in this case, but our privacy was compromised long ago, and it would be foolish to think it would be that different here.
While the FBI can access a staggering amount of technological information, this is not possible without probable cause, judicial oversight and the granting of warrants. This system of checks and balances ensures that law enforcement can harness the power of new technology to catch criminals without impinging on citizens' right to privacy.