why my mid 2012 mac air won`t shut down

Make sure you have quit all open applications before shutting down your Mac.

If you are not sure if there are any open, press Command + Option + Esc on your keyboard.

That will open the Force Quit window. Select the apps then click Force Quit

Then shut down your Mac.

Usually this is because an application or system process has crashed and will not quit or there is a corrupted data file to which the system cannot write such as a bad cache or preference file.

Try creating a new admin user account. Log into that account and see if the shutdown problem goes away. If it does, then the problem is something in your user account.

Next time you try to shutdown first quit each running application to see if they all quit properly.