In earlier releases akregator can be launched and run inside the Kontact window. But in the actually version it doesn't.
I can launch akregator, but then it comes into its own window instead to use Kontact's.

Is there any way to use the old way?

Greetings
Sascha

Can you check if your packages are all up to date, or if there are more instances of akgregator running? Also check if everything is OK under Settings > Configure Kontact, to see if you have actually enabled Akgregator there.

I've had this problem, what I found is that when I run Akregator in it's own window, it does not close properly. So I have to go into a KSysGuard and close it that way. As it does not close, when you click the side bar button in kontact, it just switches to that window.

Like some of the other Kontact apps, closing Akregator's main window via the usual window close button or Alt+F4 shortcut doesn't exit the application, but just minimizes it to the system tray (It may be hidden). To shut down the whole application you need to do one of the following: Right-click on the system tray icon and select Quit; With the window open select File -> Quit, or use Ctrl+Q. If those don't work then I'd suggest filing a bug report to bugs.kde.org.

Once the application has been shut down, you should be able to select it within the Kontact window as you expect.