How fix a MacBook Air that is not wanting to update the os El Capitan

Another option to try after you have confirmed that the device is compatible with the desired OS is to make a back up.

After you have the back up, restart your device and as soon a you hear the chime hold down CMD + R.

This will boot to recovery and you can wipe your drive and download the latest OS that Apple supports on your device.

Install it from this website: https://support.apple.com/en-us/HT206886.

If it still doesn't install then it might mean that your hardware is too old. Like, my MacBook Pro Late 2008 won't update to Sierra, maybe it's the case with your Air. Some websites manage to get older computers to run newer operating systems with some downloads that aren't approved by Apple, but I recommend that you don't use them because they seem a bit sketchy. It depends whether your MacBook Air is older than Late 2008, if it is then that is the reason why.

Here are the instructions

https://support.apple.com/en-us/HT208496

CMD+R is the keyboard keys Command and R.