My iPad 2 won’t install update

Correct, an actual iPad 2 from 2011, cannot be updated beyond iOS 9.3.5. Its simply too old.

An iPad Mini 2, can update to iOS 12.5.1

An iPad Air 2 would be the only one capable of updating to iOS 14.

Make sure you have a compatible model: link-> Identify your iPad model - Apple Support

If you actually have a nearly 10-year old, 2011 iPad 2, this will never upgrade past iOS 9.3.5/9.3.6.

Your iPad is too old for any more upgrades/updates.

Sorry.

Apple ended support for all 8-10-year old iOS devices well over 4 years, ago, in 2016.

Third party app developers abandoned and stopped supporting these 8-10-year old iOS devices nearly 3 years, ago, in 2018.

There are, virtually, NO MORE third party apps available from the iOS App Store, any longer!

None!

If you need/want an iPad with an up to date iPadOS with access to current, updated apps, then you really need to seriously consider a new iPad model OR a much, MUCH “newer” and less expensive, used iPad models, from better known, trusted Apple product/device retailers/resellers, locally or online, capable of running the latest iPadOS versions.

There are plenty of newer, older iPad models that can run the latest, current versions of iPadOS.

Sorry & Best of Luck to You!

iPad2, iPad3 and iPad mini1 can only be updated to iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular models).

Apple ended update support for these models in September 2016. Your iPad cannot be updated to iOS 10 or later major versions of iOS, as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS. This limitation cannot be bypassed; these are 32-bit architecture devices, whilst all recent versions of iOS/iPadOS are designed for 64-bit hardware platforms. iPad2, iPad3 and iPad mini1 are obsolete.

You may wish to consider that compatible Apps for your iPad are increasingly difficult to find - as third-party developers are increasingly dropping support for older versions of iOS preceding iOS11/12/13. As older versions of Apps are removed from the Apple App Store, you’ll not be able to (re)download or install them - which may severely limit the usefulness and utility of your iPad if you should you ever need reset or restore your iPad. As such, if you want or need to access most current Apps, requiring more recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model.

Of current models, even the entry-level iPad8 has specifications and capabilities that will massively outperform you current iPad - and is compatible with the vast majority of current Apps. Other models are more powerful still.

I hope this information provides helpful and succinct clarity as to your available options - and the limitations of your current iPad.