
Real reason he couldn’t save the girl: The Time Machine (2002)
It's taken me till now to realize this but what the Uber-Morlock says to Alexander is that Emma's death is a 'fixed point' because her death is the reason Alexander invents time travel in the first place. If she lived, then he never builds the machine, thus he never goes back to save her. So it creates a paradox.
Alexander does travel to the past and changes other things, though. What I think the movie is implying is that Emma's death is the ONLY thing Alexander cannot change with his Time Machine because her death is directly tied to the machine's existence itself.