Uh oh... I see another brake debate in the near future.

Fishtailing is the number one reason not to use both brakes at the same time. If you are grabbing the front brake hard enough to lift the rear wheel, you are using it correctly (maybe even a bit too much) and there's no reason to add a rear brake unless you want the redundancy in case of a front brake failure.

The fastest way to stop on an upright bike on dry pavement is to pull the front brake hard enough that your rear wheel is about to lift off the ground. To get more braking power, put your weight as far back as possible to avoid lifting the rear wheel. Because once it gets airborne, your center of gravity changes and you lose stability, making it easier to flip over.