Old Illustrator versions

For unknown reason Adobe CC app doens't allow to reinstall this version.

For some time, Adobe has had a policy of only offering the current version, and the major version immediately prior to the current version, via the Creative Cloud desktop app. They call this their "N-1" policy.

https://helpx.adobe.com/download-install/kb/download-availability.html

If you want earlier versions, you have to obtain them from other reputable non-Adobe sources. Best practice is to uncheck the Auto-update option in Preferences and, when you manually update your apps, decline to uninstall previous versions when prompted.

I do not know how far back this process will go, but try...
Direct Download Links https://prodesigntools.com/tag/ddl MAY help
-you MUST do what it says in Note: Very Important Instructions
-https://prodesigntools.com/adobe-cc-2015-direct-download-links.html#download-instructions
-the prodesign links go directly to Adobe's file server, so this process will
--only work until Adobe completely removes the old version(s) from the server
.
IF/When you do have a download, be sure to copy it to AT LEAST one external device
-since Adobe does sometimes remove old versions from the server
-a usb flash drive or external hard drive, or write to a DVD