In situations where you're turning, braking and adding (or subtracting) throttle in quick succession or at the same time, such as riding in heavy traffic, riders often find themselves caught between a rock and a hard place--or between the brake lever and the handlebar.
Think about it. For maximum braking you need at least your index and middle fingers squeezing the lever, if not all four digits. Right? It's certainly difficult to get max stoppage with the cliched one-finger squeeze.
Conversely, it's not easy to accurately control the throttle or forcefully steer the motorcycle via the handlebar with only your thumb and weakest two fingers--your ring finger and pinkie--wrapped around the bar, which would be the case if you were covering the brake lever with your index and middle fingers. (Go ahead, try it. We'll wait.)
So you probably do what many riders do: Ignore covering the lever altogether (dangerous), or cover the lever with your index finger (for a modicum of instant-on braking power) while keeping the remaining four fingers on the right grip to more precisely maneuver the bike and control the throttle.
This is a fine plan...right up until that OldsmoBuick veers across your bow and you need maximum braking right now. One finger might not be enough to stop you quickly enough, and there might not be enough time to pull a couple more digits up there to help out.
It's a difficult dilemma, one there's no easy answer for. The best advice we can give is the system many of us have adopted over the years whilst dealing with nasty L.A. traffic: Scroll back and forth between one mode (index and middle fingers covering the lever) and the other (index only on the lever), using your gray matter to decide on a constant basis which mode will best keep you from becoming grille kill--or being punted into the fast lane sans motorcycle.
Either way, keeping the brain engaged is the best way to keep the cagers at bay.