Q: Computer Itunes is version 12.1.2 and new Ipad is 10.0.2 but Itunes will not connect.  Why?

iOS 10 requires iTunes 12.5.1 or newer which in turn requires OSX 10.9.5 or newer.  Software Update only checks for updates for the current system version you are running but that itself may be out of date.  It may or may not be possible to upgrade your computer to the required system. Find your computer model on the http://www.everymac.com web site and near the bottom of the system specification section it will say what OS versions it is capable of running. If you cannot run a newer system you will not be able to sync this phone to your present computer, though some features may be available with iCloud services such as Apple Music or Match. OSX 10.9 and 10.10 are no longer available. Check this article on El Capitan (OSX 10.11) and Sierra (OSX 10.12) upgrade options https://discussions.apple.com/docs/DOC-10692   Theses systems may run slower on older machines and require additional RAM purchase (4 GB is a realistic minimum and many recommend 8GB).  Doing a big jump in system versions is also more likely to affect old software.

Snow leopard to el capitan, will it cause my macbook to be slow?  - https://discussions.apple.com/thread/7412959

Current OSX general upgrade information, including system requirements - http://www.apple.com/osx/how-to-upgrade/

If you have any PPC generation software that has been running under OSX 10.6 it will not be supported under any later system versions.

Download iTunes update --> https://support.apple.com/HT201352

You need to be running iTunes 12.5 in order to connect to a device running iOS 10. If you computer tells you that iTunes is up to date, then it is running the highest version that the computer can run.

Best of luck,

GB