Why doesn't my iphone 3g have the option to update software?

It asks me to update software in order to download apps such as facebook! But i cnt help!

Added (1). I go to settings. Then General… And the it doesn't have the "update software '' option…

You need to update iOS software to keep update of these apps. You can download the latest iOS software with iTunes or iPhone.

At iphone: Settings ->Gerneral->Software Updates

The highest iOS on the 3g is 4.2.1
You can use this tool to search the iTunes store for compatible apps:
https://sites.google.com/site/iossearch/
Here's another app search tool which I haven't tried:
https://itunes.apple.com/...74910?mt=8
And here are some 3rd party apps which are compatible with Facebook:
https://itunes.apple.com/...11743?mt=8
https://itunes.apple.com/...28125?mt=8
https://itunes.apple.com/...36714?mt=8