@CagenGamer The Origin client needs permission to be able to write files to your disk. You may have been prompted when you first ran the Origin client with some message like "Origin.app requires permission to your hard drive" and you may have accidentally denied the request. This will prevent Origin from being able to install additional apps (the games).
To check this, and to possibly grant the needed access, go to:
Apple menu -> System Preferences -> Security & Privacy
In this panel there are four tabs: General, FileVault, ,Firewall and Privacy. Select Privacy.
The panel on the left has a long list of options. Scroll down until you see a blue Folder icon with the words "Full Disk Access". Select this one. On the pane on the right will be a list of programs. Do you see "Origin.app" listed? Does it have a check-box next to it, and is it ticked?
If the check box is not ticked then you will need to enable the access. You will probably need to click the Lock icon on the bottom left, then enter your account's password. You should now have permission to tick the box next to Origin.app. Now close the System Preferences window and try to re-launch the Origin application. Does it work now?