According to this post (and to my personal experience), installing the Skype app on Facebook and the Skype client on OSX Mavericks will result in you being logged out from Facebook every time you launch the Skype client.
This question is not only to warn you of such an issue but to discuss what this could imply. It is my understanding that no third-party application should have arbitrarily access to navigation cookies: since this looks like what's happening, I'd like to know:
How exactly can the Skype client trigger such a response?
How is this not a security issue?