After downloading your browser, it quits before opening. This has happen the last 45 days and yet again today. I have tried this in Safari and Google Chrome. I does work in Windows 10, good for you.
On my MAC Book Pro I run Mac OS Catalina 10.15.5. I see from another post (June 2019) the problem is still a problem.
Here is the report, in part, from Apple.
Process: Brave Browser 
Path: /Applications/Brave Browser.app/Contents/MacOS/Brave Browser
Code Type: X86-64 (Native)
Parent Process: ??? 
Responsible: Brave Browser 
User ID: 503
Date/Time: 2020-07-25 14:03:04.024 -0400
OS Version: Mac OS X 10.15.5 (19F96)
Report Version: 12
Anonymous UUID: 619268C3-75BB-8658-9BBC-2F1FB8CFFC82
Sleep/Wake UUID: C29BED86-D49B-41C9-A485-7BF97DC7C6F6
Time Awake Since Boot: 150000 seconds
Time Since Wake: 1100 seconds
System Integrity Protection: disabled