The stories I have so far heard made it sound more like they wanted to make more money than the nonprofit NAUI was providing opportunity for rather than a problem with the training its-self. Dr. Brylske's book cites padi as being started because NAUI was "unresponsive to the needs of inland instructors". That sounded to me a lot like Ralph Erickson wanted to create the "referral" program we know today for instructors who really weren't in a place to teach scuba to get a piece of the financial pie. It also covers briefly NASDS and IDEA/FSDA.
This History of NAUI, written in part by Al Tillman (NAUI Instructor #1), sheds more light on both issues.
NAUI's leadership came from the Los Angeles County program in California, which was taxpayer supported and thus able to work comfortably as a non-profit. It could not, however, take those taxes out of the county, so they had to create a non-taxpayer-funded organization (NAUI) to go outside that county. They set NAUI up as a non-profit as well, but it never really worked well. They enjoyed free office space out of the generosity of a skin diving magazine, for example, but when that magazine was sold to a less generous owner, they had to find a new home. For a couple of years they only stayed in existence because they got a substantial loan from Bill High, later founder of PSI. They were thus always strapped for cash. (NAUI today is partially profit making, which helps.)
They were also struggling to find a way to find students. Led for a while by Glen Egstrom, a university professor, they settled on focusing on university-based classes. This very much fit the non-profit thinking. Student fees were paid by their tuition, which would otherwise have been spent on some other P.E. class, so a scuba class was essentially free to the student. The instructor got paid through the university system. While the system worked for those reasons, it was very, very limiting in growing the numbers, and it shut out a huge portion of the potential market. A lot of NAUI members did not like that approach.
In 1965, for reasons that very much included cost savings, their new leadership decided to cut back on its national approach and focus on California. In doing so, it canceled a major instructor training session scheduled for Chicago. That was the last straw for the NAUI group in Chicago, which had differed on a number of policies, including the method of attracting students. They quit and formed a new agency, PADI. They immediately began to institute a new student recruitment system by partnering with the stores that were selling scuba gear, figuring that those stores wold be the best place to get new students. At about the same time, a trade association promoting the sale of scuba gear, the National Association of Skin Diving Stores (NASDS), had the same idea and changed its name to the National Association of Skin Diving Schools. They went a step further in requiring their instructors to be associated with a store so they could be effective agents of gear sales for those stores.
The first major criticism I had about my "no kneeling class" was from NAUI corporate and then from a NAUI BOD. I was told I was endangering my students by not planting them firmly on the bottom. For reals.
