Hi Krisitie,
This is a feature of Mountain Lion in which you need to switch off it is called gatekeeper. Gatekeeper acts to stop applications being installed from other sources other than the app store. In order to switch it off follow the following steps.
1.Launch System Preferences
2.Click on the Privacy & Security icon in the top row.
3.The General tab is where we want to be.
4.If everything is grayed out, click on the lock in the bottom left hand corner and type in your administrator password. This will allow you to make changes to your settings.
5. Under the heading "allow applications to be downloaded from" tick the bubble next to anywhere
6.Once you've made your changes you can go ahead and exit out of System Preferences altogether.
7. Install Activinspire
Regards Kyle