why can't i install the newest version of iPadOS on my iPad Air 2? I only have 13.7

The IPad Air 2 should be able to update to iPad OS 15.2

iPad models compatible with iPadOS 15.2 – Apple Support (UK)

As you are having difficulty updating your device, you should check out the resource below

If your iPhone, iPad or iPod touch won’t update – Apple Support (UK)

Make sure that your iPad is setup to meet the following requirements before you attempt to update the iOS version over a Wi-Fi Network.

• Your iPad must have a fast Wi-Fi connection; you cannot update over cellular data or a cellular hotspot
• Ensure that you do not have a beta profile installed from a previous version
• The iPad can not be in Low Power mode
• The battery state of charge must be above 50%
• Your iPad must have at least 6GB or more free storage space
• Your iPad cannot be connected through VPN
• You should leave the iPad plugged in until it finishes updating, both to assure that it remains above 50% and to keep Wi-Fi enabled (Wi-Fi turns off when the phone sleeps if not connected to power).

Axel F.

Your iPad is too far behind in iPadOS upgrades/updates.

If you have access to a full computer, like a Mac or Windows PC, try either using the Finder on a Mac that has the newest macOS Catalina, or later macOS, installed OR with an older Mac with an older Mac OS, download and install the latest iTunes version ( or latest iTunes for Windows PC ), make sure the Mac or Windows PC is connected to the Internet, connect your iPad by the USB charge cable to the computer and let the iTunes application upgrade/update that iPad model, using the iTunes Software Update feature, to its current, maximum iOS of iOS 12.5.4/iPadOS 14.6

Make sure your iPad is, at least, charged to 50% or greater to attempt this.

Also, make sure to do a backup of your iPad's data, prior to upgrading/updating.

Backup to Apple iCloud and/or a full Mac or Windows PC using the same iTunes app OR, if a newer Mac running macOS Catalina, or later, making a backup using the macOS Finder app.

If NO access to a Mac or Windows computer, you will have to seek help from a good friend or family member, with a full Mac or Windows PC, to help you out

OR

Search online to locate and call contact your nearest, “local” Apple Store location to try/attempt to make an appointment to get your Apple iPad upgraded/updated to its latest iPadOS 15 version.

Apple Store employees will be glad to help/assist you.

Best of Luck to You!