surface boundary doesn't match the curve
 

Thanks, guys! I turn on "show full" and it works!

Also, I've found another way to do the segment: Repair Goemtry->Build Diagnostics Geometry. Then build from the curves and the surface.

After that, the curves will trim the surface, and they are associated to the surface as well! This is useful if you are going to do an unstructure mesh, and useful for automatic meshing.