Could you please put Illustrator CC 2015 back on download option?

they are keeping you from using 2015 because of expired licensing. they no longer have licensing to third party stuff used in older versions and therefore they can't legally distribute it. 

Hi Xiaonan,

Sorry to hear about the trouble you are facing with Illustrator. I am afraid to say that we don't have an option to download the 2015 version of Illustrator however we can surely help you with the latest version. As suggested above it could be a plugin issue because of which the Illustrator is crashing. To cross-check that, will it be possible for you to try booting the system into Safe Mode (https://helpx.adobe.com/in/x-productkb/global/start-safe-boot-mode-mac.html) and check how it works there. It starts your system so that it performs certain checks and prevents third party software/ services from automatically loading or opening. If it works fine in Safe mode, then there is some third party service or application like antivirus, plugins or web extensions which are conflicting with the Illustrator. 

Regards

Rishabh

By the way, my guess is a plug-in. Do you have any 3rd party Illustrator plug-ins? If so, try without them.

It is impossible to install older downloaded software on Catalina due to Apple's rules. Even if they had not, Adobe have removed Illustrator 2015 from licensed versions.