Edit: After half day, my wife’s Mac started having the same problem. I have then applied the solution that I found in the Apple
How to Get iOS 6
As the world gets ready for the official release of the iPhone 5 on Friday, Apple have already made iOS 6 available for download. While it will already be installed on the iPhone 5 as well as any subsequent devices from now on, it is also compatible with most of their other current products, including all the iPhones from the 3GS onwards, the iPad 2 and its third generation successor, and the fourth generation iPod Touch. If you own any of these then it is worth downloading the update, especially since it is free.
The first step to getting iOS 6 is to wait a day or two. While this isn’t compulsory, you will have to deal with some heavy traffic if you try to download it straight away because it has only just come out and everyone wants it!
The first real step is to update iTunes to version 10.7 if you do not already have it so that you can use it to back-up your device. While iCloud is also an option, iTunes will provide you with a lot more free space, while iCloud charges if you exceed 5GB. Of course, the choice is yours. Updating iTunes is as simple as opening the application, clicking on Help and then selecting Check for Updates.
Next you need to back up your device, which you can choose to do either with iTunes or iCloud, whichever one suits you the most.
Now we can get to the update itself. You can get iOS 6 either over the air if you have a good enough Wi-Fi connection or through iTunes, which may prove much quicker.
To use Wi-Fi, go to your device’s Settings, select General and then Software Update. iOS 6 will pop up with some accompanying information and a button labelled Download and Install. Click it and your device does the rest. This can take time though so you need patience and at least 50% of your battery left. Better still, plug it in to be safe. Your device will restart and install iOS 6 automatically when the download is complete, although you will have to work through the setup screen to complete the process.
Alternatively you can download it through iTunes on your computer. To start, connect your device to your computer with its USB connector cable and open iTunes. Then you need to find the name of your device on the left side of the interface and click on it.
When your device information appears in the middle of the screen you will see a Check for Update button, which you need to click.
You will then be informed that a new update is indeed available while a Download and Update button will do the rest when you click on it.
The update will take some time so you need to be patient and leave your device alone while it updates. Once it reboots your device will have iOS 6 and all the shiny new features will be ready for you to play with.