Tim Cook is right on this one... We really, really don't want the government to be able to get access to our devices. Smartphone owners, for the most part, have no idea how much information is on their phones. The phones know where you've been, what calls or messages you've received and sent, possibly intimate photos and video, and (depending on the apps installed) may also know every key you've pressed, every web site you've visited, and even may record your conversations! It's no surprise that the government would like to have access to that. There's also no doubt that having access will help them convict guilt people. The problems start arising when you consider how it could be used to help convict innocent people (as every new law enforcement technology has done), and how it will be misused and abused.
I read an example not long ago of such misuse, but I couldn't find the article. The gist of it was this: a woman was murdered in a brothel, in Mexico. The woman was a famous celebrity of some sort, and there was enormous pressure to find the murderer. The police started examining the smart phones of anyone they arrested, looking at the GPS records in the phone to see if they'd been at the right place, at the right time to have committed the murder. A few weeks after the murder, they stopped a businessman for speeding – and after examining his phone, determined that he'd driven by the brothel at the right time. That evidence was presented to the jury, and he was convicted and sentenced to life in prison. What the jury was not told was that he had driven by at 70 MPH! The story I read was of his appeal, and of the fight this man is going through to have that latter bit of information presented to the appeal jury. That's the sort of thing one can look forward to if the government has easy access to the trove of information in smart phones...
The New York Times, of all places, has a reasonably balanced overview of the issue. There's much more, all over the web, ranging over the entire spectrum of possible responses...