I am on 13.1 and iMessage crashes immediately upon launch. Telling it to try again does not change the result.

With the Application completely closed.

Hold the SHIFT key and attempt to launch the application.

This is a Safe Launch of the Application

Still issues >>

1 - Restart in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Safe Mode will also eliminate Third Party Software, extensions and drivers from loading 

3 - Does the issue present in this mode ?

4 - Sometimes a Safe Boot followed by a Normal Boot will just put things right.

Still issues >>>

5 - If not - there could be something in the main User Account playing up. To further isolate this - Set up users, guests, and groups on Mac. Then log out of the Main User account and log into the dummy account and test again if the issue persists.

6 - If the issue is present in the dummy account - then, this appears to be a System Wide issue on the computer.

Still issue ➡️

7 - Download the Application Etrecheck directly from the Developer.

This is a Diagnostic Tool that makes no changes to the computer.

It makes a coherent and readable inventory of both the Hardware and Software used on the computer 

The application is free or paid from added features. 

The Report will Not Reveal Any Personal Information. 

Post back the Full Report - copy and paste - >>>> using the Additional Text Icon ( 3rd Icon to last ) <<<<

We can have a look at the report for possible issues and may have possible suggestions to resolve the issues.

Then perhaps the User ( you ) is better by opening your own question

Writing an effective Apple Support Communities question

By opening your own question, the user may get better individualized assistance from a whole group of well informed and experienced Contributors.

Joining a previously exiting question like this one, tends to not get the attention the use may want / need for their computer issue