There are many reasons why O365 external invitations could fail, but most are obvious reasons…expiry, using non-Microsoft public emails, etc.
However there is a scenario where the sender and receiver both have done everything right and security settings are set correctly and yet invitation fails.
If this happened to me, I would loose my mind trying to figure out what the problem is!!!
Fortunately someone else has run into this problem and took the time to document the issue and possible resolutions…