The flaw SAE was built to close
WPA2-Personal had one structural weakness: everything descended from the passphrase. Record one 4-way handshake, take it home, and every guess of the password can be tested offline, billions per second, forever. Strong passphrases survive; human ones often don't.
SAE — Simultaneous Authentication of Equals, the Dragonfly key exchange — removes the thing the attacker needs: an offline test. The password never produces transmittable proof. Instead it seeds a position on an elliptic curve from which both sides build commitments mixed with fresh randomness. Each side proves it reached the same shared secret; the secret itself depends on randomness that dies with the session.