I can't install Creative Cloud App on my Mac

Have you logged in to Mac as Administrator ??

Step 1)

Click on the Finder and look for the options listed next to Apple Icon located at the top left corner of the Desktop screen and click on "Go" menu button and select "Utilities" option.

(Applications>Utiliites)

" If present "  Adobe Creative Cloud and Adobe Application Manager folder under Utilities window and trash both folders.

Step 2)

If present,  Trash Adobe Creative Cloud folder from Applications as well.

Step 3)

Click on the below link and download & run Adobe Cleaner tool :

If present , Select the option "Adobe Application Manager for Mac OS X 10.6" and then click on "Clean up Selected" .

http://download.macromedia.com/SupportTools/Cleaner/mac/AdobeCreativeCloudCleanerTool.dmg

Step 4 )

Click on the below link and download Adobe Application Manager and install the same :

http://download.adobe.com/pub/adobe/creativesuite/cc/mac/ApplicationManager10.0_all.dmg

Once the installation process is completed, installation box will disappear, then open Application folder and locate Adobe Application manager launch icon , double click on it and update .

Once the update is completed. It shud launch Adobe Creative Cloud app.

Still same ??

You need to try from different user account   or it is better to enable Root user account and later you can disable it.

I had mentioned steps to enable Root user account in below link :

Re: Why isn't photoshop downloading?

After logging in to Root account , try to install Adobe Creative Cloud app , it shud work.