I started my climbing with Prusick hitches one short at the mid attachment and one below that for my foot. I ascended with that and switched over to a Rack to descend. The Fire school believes it was best to learn that first before moving onto using hand ascenders and a Rescue Eight..... now they teach chest ascenders with Hand ascender and I'Ds or D5s.
Every climbing field has their own thing but all make the same fundamental mistake in terms of teaching climbing IMO. They all teach to a preconceived notion or book method/accepted way. But, where is the harm in taking the extra step as the instructor and finding what is best for the new climber? I can argue to those that say you must know Dbrt first in climbing that you are wrong. I and a lot of others didn't. We learned SRT caving/rescue techniques first before " having to MUST KNOW Dbrt". And be told at that time SRT can't be used in tree work because it just won't work.....
Here is my point, there is no one and only way to first learn climbing. If a person is more comfortable on Dbrt at first then that's the answer, if SRT then that's the answer. Let them and their natural abilities tell you the direction to start in. Then build on it after. But, as the instructor you should know climbing and people very well to make that call. If you can't then it may be a good idea to step back and really ask yourself if you should be teaching.
P.S. There is a whole HUGE industry that only teaches SRT and they do just fine starting off. Although when I mention Dbrt techniques they give me the same bellyaches as some tree guys with learning SRT when new and young.... think outside the small box we were given and truly learn climbing all around.