From Skype 2.7 on Mac the startup has changed. It used the general system startup settings rather then a separate preferences for Skype. This means you can’t set it in the Skype preferences.
To set Skype to open at startup Ctrl+click on the Skype icon in the Dock and check the “Open at Login” under Option.
To stop Skype from opening at startup follow the same instructing and make sure you uncheck the “Open at Login“.