He didn't do Terminator 3 because he thought that Terminator 2 was the end of the series. He filmed an ending where the war was stoped. I saw this scene my opinion it was horrendous. I like the idea of the Terminator series as a neverending loop where Kyle was always his father and the future is set. But go figure he didn't want to do it. He still appears to have intrest in the first two films why he keeps creating more and more versions.