There are several possible reasons why Skype for Mac OS X might not be starting.
The most common cause is that your system does not meet the minimum requirements of the latest version of Skype. For more information, check this page.
You should also make sure that your version of Mac OS X is up to date by using Software Update and installing the latest version of QuickTime.
Another common issue is with the default text-to-speech setting on Mac OS X. To change the default text-to-speech setting:
- In the menu bar, go to the Apple icon > System Preferences... The System Preferences window opens.
- In the System section, click Speech. The Speech pane opens.
- Go to Text to Speech and in the System Voice drop-down, select anything other than the current selection.
- Try to start Skype again.