macOS Catalina was the first version to drop support for 32-bit apps entirely. If you are trying to run very old "Legacy" versions of Illustrator (CS6 or earlier), they will because they contain 32-bit components. Performance:

This paper examines the specific technical relationship between Adobe Illustrator and macOS Catalina (10.15). As the first macOS version to drop support for 32-bit applications, Catalina presented a critical pivot point for creative professionals. This document analyzes the impact of the transition to 64-bit architecture, outlines the compatible versions of Illustrator, details common stability issues specific to this OS environment, and provides migration strategies for legacy workflows.

To get the most stable experience possible, perform this checklist:

: Adobe recommends updating to the latest 64-bit compliant versions, typically Illustrator 2020 (v24.x) or later, for full compatibility. Unsupported Versions