They'll never understand

I don't know if it helps, but this is not really a lie, and you shouldn't feel bad about saying it. You have your own reason for not being able to do something you committed to. Someone else might have a different reason that is equally personal that they don't want to share. "I forgot and I'm sorry" is a socially acceptable way to take responsibility without sharing specifics and potentially making someone else feel confusion or pity.

You can still work on the "why wasn't I able to do the thing I felt I needed to do" without worrying about "why wasn't I honest about my reason".

Just my two cents though.