The iPad 2, 3 and 1st generation iPad Mini are all ineligible and excluded from upgrading to iOS 10 AND iOS 11.
They all share similar hardware architectures and a less powerful 1.0 Ghz CPU (with the iPad 2 and the 1st gen Mini, a paltry 512 MBs of RAM, too!) that Apple has deemed insufficiently powerful enough to even run the basic, barebones features of iOS 10 OR iOS 11!
Why would you want to upgrade, anyways?
Since iOS 8, older iPad models such as the iPad 2, 3 and 4 have only been getting the most basic of iOS features.
Older iPad users get none of the newest and coolest cutting edge features that newer model iDevices, with better hardware specs, can handle with more aplomb.
Plus, the iPad 2 and 3 are the only two supported models left that use the much outdated 30 pin dock connector.
The same iPad 2 users who whined and moaned and groaned that both iOS 8 and 9 slowed down the performance of their iPad 2 models would come back, once again, in even angrier droves, with even more complaints of slowdowns under iOS 10 or iOS 11.
You would NOT be happy with your iPad 2 speed and performance under iOS 10 or 11, if you could run it.
Just because your iPad 2 is no longer able to upgrade to the latest iOS doesn't mean your iPad 2 is suddenly useless.
Your iPad 2 will work as it always has and the apps you have installed on it will continue to update and receive some level of app updates relevent to your current iOS.
You have had four years of iOS upgrades and updates.
Your iPad 2 will still do everything it does now and you will, get, at least, another full year, perhaps two, if you decide you want to wait longer to get a new or newer iPad model.
Your iPad 2 is NOT, suddenly, becoming obsolete or useless.
So, your options are really keep using your iPad 2 or purchase a new iPad if you feel you need or want to.
Your current iPad 2 will still work and continue to receive app updates for some time, when, with the current iOS 11, ALL support for older 32 bit iDevices and any iOS 32 bit apps will come to a final end.
Your iPad 2 will still work and function as it always has, but will no longer receive any more app updates some time in the foreseeable future.
The final app updates your iPad 2 will end up receiving will be their last!
Your iPad 2 should STILL be receiving app updates, currently, but look for this to end sometime soon.
This is why Apple introduced the new, lower cost 2017 iPad 5 model, in April
Apple is trying to get older iPad 2, 3, 4 and 1st gen Mini iPad users to upgrade to more modern iPad hardware in anticipation of the introduction/release of iOS 11, which WILL render all older 32 bit iDevices obsolete, in time.
Good Luck to You!