Why isn't syncing isn't available in recovery mode?

I am trying to download ios 7 to my iphone 5, but syncing and backing up seems like it is unavailable every time i go into the device tab. I was told to download the latest itunes version 11, so i did. But it doesn't work any more different than the version 10. Right now my phone is in recovery mode and my phone's screen says i need to use my usb and plug it into the computer for itunes. When i open up itunes, it says the phone is up to date but the only button i can press is restore. I need to sync/back up my contacts before i restore my phone but it won't let me! HELP!