"The first time I was molested was at the age of either six or seven," Stewart told CBS News Correspondent Sandra Hughes. "I was molested all the way up until I was 18 years old."
Stewart and his brother Tom were sexually abused by their assistant Scout master.
"The nightmares are still very real, even 25 to 30 years later," Matt said.
Former troop leader Bruce Phelps admitted under oath to having sexual contact with one and then the other.
As part of a lawsuit against Phelps and the Boy Scouts of America, the Stewarts' attorney, Tim Kosnoff, got an unprecedented look inside thousands of secret files through 2005.
"I was blown away," Kosnoff said. "It was staggering."
Kosnoff analyzed the numbers and came to this shocking conclusion: Before 1991, "a Scout leader was being tossed out for child molestation at the rate of one every three days," he said. "Post-1991, the rate was one every two days." That includes people suspected of abuse.
The Boy Scouts of America would not confirm how many troop leaders it has had to dismiss, but released a statement saying, "The total number of individuals in the file is an extremely small percentage of the tens of millions who have served in BSA since 1910."
Criminal background checks are now required for Scout leaders, and adults are prohibited from being alone with a child.
The organization claims its child abuse prevention program is the best in the country. However, in 2005 the man who ran that program, Douglas Smith Jr., was sentenced to eight years in federal prison for trafficking in child pornography on the Internet.
"The Boy Scouts of America is not a safe place for your boy," Matt Stewart said.
These days the entire first chapter of the Boy Scout handbook is dedicated to child abuse prevention. In it, children and parents are told that although Boy Scout law may emphasize obedience, if an adult asks a scout to do something uncomfortable, that's a rule that's OK to break.