Q: My computer keeps telling me to update Pages, but when I go to the App store, it won't update, I just get the spinning wheel.

The specific release of OS X (Apple logo : About this Mac), and the specific version of Pages (Pages : About Pages) will keep us from guessing.

When I go to the App Store > Updates, there is not even an update available for Pages?? I still continue to get the message there is an update almost every time I open the App.

OS: 10.11.6

Pages: 5.6.2 (2573)

Whenever Apple updates the App Store with a new version of Pages (v6 now), the older applications will whine about a new version available. However, you will need macOS Sierra installed to obtain the new Pages v6, as it is not available for older operating systems.

Well, I use an "old version" of Pages, specifically Pages 4.3, on Sierra. There may be some features that no longer work as they used to pre-Mavericks (when Pages 5 was inflicted on the public) but none that affect me in my daily use.

Use what works for you. Personally, I prefer Sierra over El Capitan for reasons not related to iWork. El Capitan has a nasty habit of freezing & bringing down my whole system. It even made an internal SSD "vanish" & it had to be replaced.

deleted - duplicate

You can turn off the nagging:

Menu > Apple > System Preferences > App Store > uncheck Automatically check for updates

Peter