AFAIR, they changed communication model from Peer-to-peer to client-server and then it all started. Why did they need all conversations to pass through their servers...? Something is hinted in the last paragraph of this article though:
Clients server with message history on the server solves a lot of the weird message ordering things that would happen when you had conversations between multiple users each with multiple clients that were mostly offline. This is especially helpful for mobile, since always online mobile isn't realistic.
It certainly also enables some law enforcement use cases though.
This is the VirnetX patent case which is still partly ongoing. It's kind of difficult to find but it involves patents 6,502,135, 7,418,504, 7,921,211 and 7,490,151.
https://www.lifewire.com/skype-changes-from-p2p-3426522