Why would an endodontist give up on doing a root canal before he finished it?

Something gone wrong. He wouldn't unless something went wrong, or is more complicated than originally thought, if simply gives up, and doesn't explain, and doesn't make an appropriate referral, (s)he has not performed service correctly. Go back to your general dentist, or find a good one if don't have. Important (opinion): for dental or general health problems, always c good generalist first (topic 4 blog 2 come).
Give up? I can't imagine a specialist giving up if there is any chance of completing the therapy. Possibly there is a blockage in the tooth canal she/he cannot negotiate. I think you should ask more questions about what comes next - possibly the doctor hasn't 'given up' but needs to use a different treatment choice to complete the care because something unexpected happened.
Several reasons. Root canal therapy is often successful, but not always. Not all teeth can be saved. An endodontist might give up on doing a root canal for several reasons....The tooth might be fractured, the decay may be too severe-down to the bone, the canals may be too calcified, the anatomy of the canals may be too complex....And others.