In fact, why does CocoaPods not install the latest version of pods?

Basically, it respects what you say in your Podfile.

You have several options (from CocoaPods guides):

• > 0.1 Any version higher than 0.1
• >= 0.1 Version 0.1 and any higher version
• < 0.1 Any version lower than 0.1
• <= 0.1 Version 0.1 and any lower version
• ~> 0.1.2 Version 0.1.2 and the versions up to 0.2, not including 0.2

You can also provide no version at all, which will install always the latest available. Another option is provide a specific version, so that version will be always used.

CocoaPods cached your current version of pods, so basically you have to clean cache.
You can make it locally in your project directory using this command:
pod cache clean --all