Have you installed the 6.0.2 patch? Does it work in a new user account on the Mac? If it works in a new user account, see Adobe Forums: InDesign crashes at startup for a list of things to delete from the original user and see if that solves it.
CS6 is not supported under El Capitan, but you can try turning off autohide menu bars in the system preferences.
InDesign crashes on all user accounts.
As for El Capitan. InDesign was crashing before I updated to it. So, same difference. I don't know. Back up everything, wipe the disk clean and reinstall system?
I hate to raise a conspiracy theory here. But it does seem strange that I am get this problem after trying to remove CC software. Adobe really wants us to migrate to the subscription it seems to me. I would, except my company has not gone that way. If Adobe would make it possible to save a file to a previous version, then I would go for the $20/month. But they insist on this all or nothing approach. Meanwhile, I am out one, two day's work.
You're running on an unsupported system with software that's pushing 4 years old.
There's no conspiracy and I told you what to try. If that doesn't work, trash your prefs. Then uninstall, run the cleaner tool and then reinstall.
Then roll back to a supported operating system. CS6 will NEVER be updated to run on newer operating systems.