In your Adobe application preferences, ensure "Auto-Update" is turned off.
To run Adobe Illustrator natively on macOS Catalina, you must use version 24.0 (Creative Cloud 2020) or later. These versions were explicitly rebuilt to meet Apple's 64-bit criteria and notarization security requirements. Adobe Illustrator CC 2020 (v24.x) adobe illustrator macos catalina
If you are still using a perpetual CS6 license, you must move to a Creative Cloud subscription to get a version of Illustrator that functions on modern Apple hardware. In your Adobe application preferences
: Minimum 1024MB VRAM (2GB recommended) with Metal support. adobe illustrator macos catalina