For decades, Mr Matheson - a Mormon - ran retreats offering therapy to suppress or manage sexuality, - claiming to help people live as straight men rather than gay.
In an exclusive interview with this programme he's now conceded that the practice, which almost 700,000 Americans have undergone, is not only built on a harmful philosophy but should be banned.
We are also joined from New York by Chaim Levin, who twice attended retreats co-founded by David Matheson.