Basically, back then Arnold was desperate to revive his movie career, so he had his people look for ways to get T3 made, and they found Ann Hurd who has the rights to make the movie, and she hates her ex hubby, who never wanted sequels to his final Terminator movie, the T2, which he made as a finite end to the series, but oh well the hollywood machinary was cranking, so they got the person with the rights to the franchise, and found a fanboy director who thought he could pull it off, and got the money together and made the thing, logical storytelling and intentions of the creator be damned.
The end.