I chose my school and degree based around staying close to home to help with my disabled brother. It turned out to be a poor decision, academically that is, as the course combined software engineering students with business I.T and we weren't covering anything I didn't already know. I got a summer placement writing code and realised I was learning much more during that time, so when they asked if I wanted to stay on, I accepted.
It could be viewed as not being able to complete the degree, on the other hand would it have been a good choice to persevere with a bad decision just to prove I could? I'd be concerned with working with people who couldn't admit to making a mistake, then making the best of it. Or those who refused to see the grey areas.
Admittedly the value of a degree has likely been diluted in recent years given that college standards seem to be getting more relaxed, but that doesn't mean that it's not still a somewhat useful signal, especially when you have to filter hundreds (if not thousands) of resumes for a single position.
Just like nobody ever got fired for buying IBM, no one got fired for hiring the candidate with a degree. Believe it or not, there may be more reasons behind this than 'self doubt' and 'insecurities'.