So I'll pick three examples, and forgive me for picking obvious ones, but this is just for illustration:
ISSUE 1: Flutter vs. Frog Kick. In my PADI openwater course, I was taught only to flutter kick, meaning, long slow vertical (up and down) kicks using the large muscles in the thighs and hips. This comes naturally to most people and unless they are taught something different, that's how they are going to kick. But when you're diving in Puget Sound, there is no better way to completely stir up the deep silt that covers much of the bottom than to flutter kick. Flutter kicking drives water downward and upward on every stroke and thus, in certain environments, it leaves a huge cloud behind you. It happens every dang time. (In a wreck, the flutter kick also brings a shower of debris down from the ceiling to mingle nicely with the crap stirred up from the floor, but I digress)
And perhaps there is nothing wrong with this, unless a) there are other divers in the vicinity who you have just silted out, b) you decide to turn around and happen to head back the way you came and end up in your own cloud of silt or c) you have some kind of charlie foxtrot occur in the middle of your dive, the team stops and tries to deal with it, and the silt cloud you created catches up with you and suddenly you're in zero vis.
DIR poses the hypothesis that learning to kick in ways designed not to stir up silt or rain down debris is, well, good.
So, why does frog kicking work?
It uses your fins to propel you forward by pushing water from side to side, not up and down. Combined with horizontal trim, it keeps the water movement off the floor and ceiling entirely.
ISSUE 2: Horizontal Trim vs. Vertical or Semi-Vertical. DIRF teaches you to dive horizontal in the water at nearly all times and not to use your hands to maneuver. Why? Several reasons, not all of which I will attempt to explain, but they include: efficiency of effort, more accurate buoyancy control, much less resistance through the water, more even offgassing of nitrogen in all the compartments of the body during deco stops, and more efficient use of lung/alveoli surface in the exchange of blood gasses during deco stops. (The most important reason, however, is that you look cool. way cool.)
ISSUE 3: Split Fins vs. Jetfins. Here's an equipment issue. Split fins are touted as being easier to kick (meaning flutterkick) and the fins for moving fastest through the water. This might very well be true. However, on most recreational, cave and wreck dives, getting from point a to point b in a straight line and in the shortest amount of time possible is not usually the goal. And if you make diving with horizontal trim and using the DIR kicks described above, you must have traditional fins.
I have done, or attempted, all the DIR kicks in split fins. It's doable with the exception of the back kick, though I admit that my ability to fin backwards still leaves alot to be desired. I have yet to see someone kick backwards successfully in splits. The other kicks, when done using split fins, are a) harder to do and b) not done as cleanly. Why? It's not because split fins suck. It's because frog kicks are smaller, more controlled movements and actually require more resistance against the water, not less, in order to propel you forward or backward or spin you around on a dime. This is also one of the reasons why frog kicking requires alot less effort and is much more efficient than flutter kicking.
Don't believe me? Learn to frog kick (properly!), then dive to a consistent depth, read your gauge, note your psi, and frog kick for, oh, 5-10 minutes. turn around, read your gauge, note your psi, and then head back, this time flutter kicking to your heart's content, for the same amount of time. note your gauge at the end and see if you consumed more air in one direction or the other.
And make sure to do the flutter kick second, because otherwise, you'll be swimming through your own silt on the way back.
So. There are my three examples.