The NeverEnding Story:
Though the scientist phrases it differently ("aware of your own worth"), clearly it is righteousness that will allow a person to pass through the sphinx gate. There's even a little shot at the "white-washed tombs" of pharisaism (Matthew 23:27) when the "fancy" looking knight gets his.
It is a staple of fantasy books and movies for there to be a "chosen one," who is pure, even though those around him don't know it. Arthur is able to pull Excalibur out of the stone, Aladdin is a "diamond in the rough," and so on. Atreyu, at first, seems to follow that mold...but then the Sphinx's eyes start to open! Even Atreyu is revealed to be impure, and it's only his cat-like reflexes (and some pretty severe limitations on the eye-shooting abilities of the sphinxes) that allow him to escape with his life.
For the sphinxes, nothing less than perfection will do. This is true of God. The sphinxes can see right through a shiny (righteous-looking) exterior and see into your heart. This is true of God. No one is worthy, not one. Not even Atreyu. This is true of all of us. Finding ourselves at this crossroads, where requirement meets ability, and lacking the quickness of Atreyu, we must rely on a savior from outside ourselves who, as St. Paul says, "at just the right time, while we were still powerless, died for the ungodly."