insufficient storage error while updating installed apps
Why?

You said: System storage Available space: 22.47 MB And Facebook app size is around 13MB. So why doesn't it update? It's because NOT ALL of the system storage is available for your Apps. Some space is reserved by Android. So unfortunately, you can't install Apps in that space.

About the space in SD card,

a. Facebook App is phone memory only app (Annoying!)

b. Mostly, your apps will be first downloaded to phone memory and then you can move them to SD card. So even if the app is movable to SD card, you will need phone memory to first install it!

Solution:

Now the solutions. Try these steps:

1) Move all apps (that can be moved) to SD card. You can do it from Settings or use App2SD for the same.

2) Clear cache. Again I would suggest to use App2SD for the same. This should free up good amount of space.

3) Uninstall apps that you don't need anymore.

Another suggestion I have is to install a custom ROM that takes less space on your phone.