The word does its work before anyone argues. Call something a barrier and you have already located it: in front of the person stopped, theirs to climb. Schools used it that way for years without saying it aloud. The reading scores were low because something in the child was in the way.
Section 1703(f) wrote the word into federal law and left it undefined. It took eleven children from Ann Arbor to make a court say where the barrier actually stood. Not in their mouths. In the building. The grammar was never the obstacle. The obstacle was an institution that would not learn what its own students already knew.
A barrier is real. The question the record answers is who built it, and who was told to climb.