The iPad 2, 3 and 1st generation iPad Mini are all ineligible and excluded from upgrading to iOS 10.
They all share similar hardware architectures and a less powerful 1.0 Ghz CPU, plus the iPad 2 and 1st Gen iPad Mini only have 512 MBs of RAM, that Apple has deemed insufficiently powerful enough to even run the basic, barebones features of iOS 10.
Why would you want to upgrade, anyways?
Since iOS 8, older iPad models such as the iPad 2, 3, 4 and the original iPad Mini 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.
FYI,
Just because your 1st gen iPad Mini is no longer able to upgrade to the latest iOS doesn't mean your 1st gen iPad Mini is suddenly useless.
Your 1st gen iPad Mini 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 1st gen iPad Mini 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 1st gen iPad Mini is NOT, suddenly, becoming obsolete or useless.
Good Luck to you!