Apple doesn't officially support installing Windows 10 on MacBook Airs older than 2012. But it works just fine, once installed. The question is how to do the installation...
Here's the full story (you can skip it and just read the instructions):
Wrong approach #1: Your Air has Yosemite or older. The Bootcamp of those versions actually don't care which version of Windows you try to install. So you download i Windows 10 ISO, get your reasonably large USB drive and get started. The Bootcamp assistant happily downloads Windows support files, formats the USB drive and copies Windows installation files. However, after a while copying files the process fails saying the USB drive is out of space. It is not. However, the Bootcamp Assistant formats the drive using regular FAT and one of the Windows installation files is larger than 4 GB. There is no way of pre-formatting the USB drive with exFat or making Bootcamp use anything else than FAT.
Wrong approach #2: In Mojave and later Bootcamp uses exFAT. Mojave doesn't install on your 2011 Air (it won't go higher than High Sierra). But you have a newer Mac with Mojave and use that to create the Windows installation USB drive. Installing Windows 10 on the MacBook Air kind of seems to be working, but it freezes frequently and/or blanks the screen and the installation can't complete. Turns out the Bootcamp Assistant installs drivers for the specific Mac hardware where it's run. The drivers for the newer Mac doesn't work on the old Air.
Wrong approach #3: Let's install Windows 7 and upgrade from there! Download High-Sierra (not that easy on a newer Mac since the Apple site will just redirect you endlessly, but direct links can be found on Google). Problem is that Windows 7 also has an installation file bigger than 4 GB.
Workaround phase #1: There's a built-in hack in FAT where you can split large files into chunks and fool the computer it's still one large file. Nice guy Tim Perfitt has made a Mac application that will do that for you - you feed it a Windows installation ISO and will get one back that can be copied to a FAT partition. It says it's for Windows 10 ISOs but it works for Windows 7 as well. With the converted ISO Windows 7 installs just fine on the old Air. Since you are aiming for Windows 10 you don't need a Windows 7 key, just skip the product key input. You do need a Win 10 key of course. Make sure you also create a separate Windows support files USB drive in BootCamp Assistant.
Workaround phase #2: Once Windows 7 is working, install the Windows support files installer from the separate USB drive. Then run Windows Update. Then run it again, and again and again. Run it until no more updates appear. Then run it again. Using the Windows 10 Media Creation Tool to update Windows 10 won't work, it will fail with an error message:
an unknown command-line option [/DynamicUpdate] was specified. What you need to do is create a Windows 10 installer USB drive, open a command prompt, and run setup.exe from there. Doing that will provide you an option to not activate automatic updates (you can activate that later). Lo and behold, Windows 10 installs! Once finished, install the Windows support files again. In just 1 bapillion steps you have installed Windows 10 on an old Macbook Air.
- Obtain a Windows 7 ISO.
- Use Boot Camp ISO Converter to convert the ISO to make it installable on a FAT partition (which is used by High Sierra).
- Use BootCamp Assistant to create a Windows 7 medium, download Windows support files to a separate USB drive and partition your HD. You have to do all of this on the computer you are installing Windows on (creating a medium on another Mac will bundle the wrong drivers).
- Install Windows 7 using the medium.
- Run Apple Software Update and Windows Update until no more updates are available. This means running especially Windows Update many many times, and manually checking for new updates until it's really finished.
- Use the Windows 10 Media Creation Tool to make a Windows 10 USB.
- cd to the USB drive. Run setup.exe
- Choose to change update alternatives and select not to do automatic updates.
- Install Windows 10.
- Install the Windows support files from the separate USB.