That's the advice I got from many helpful drummers back when. At first I took it to be gospel, and so I struggled to shift my focus away from my dominant right hand and to lead instead with my non-dominant left. It was not pretty. Now here I am years later, and I still find it nearly impossible to lead with my left hand under most circumstances. I regularly practice leading with my left, but my brain continually says, "Ain't gonna happen".
I have two ‘aha’ lessons from this. The obvious one is that my right-handedness wiring is very strong. Despite years of trying to force my left hand to take the lead, I’m still almost entirely right-handed when holding a pair of sticks.
The other ‘aha’ is that the time I spent fighting against my internal wiring was not time well spent! What if I'd spent that practice time doing something useful, something that would have brought me a better return on my investment?
Once again I turned to the pros -- the greats -- to see if they could shed some light on the issue. I love YouTube because you can find just about everything ever recorded in seconds. So I called up dozens of videos ranging from Chick Webb and Max Roach to Buddy, Gene and Louie to Dave Wekel, Steve Gadd and a host of others. Almost without exception, I found that these players work mainly off the dominant hand. Yes, they all have ferociously powerful and useful non-dominant hands, but on closer examination you’ll see that the right-handed tend to lead with the right almost all of the time.
So why fight it? Instead, look upon your dominant-handedness as a strength. It’s great at leading, so let it. Let it be your main speaking voice. Yes, it’s important to work at building up your lesser hand, and if you can make the switch to ‘other handedness’, great, but it’s not necessary. Over time your other hand will become as strong and as useful as your dominant hand. And if that hand remains merely a ‘helper’ to your dominant hand, well what’s wrong with that? Your hands are a team and the best way to manage a team is to focus on a member’s strengths rather than try to force it to become something it wasn’t meant to be. Of course you also make your team practice -- a lot -- and encourage them to work on their weaknesses.