Just the facts...
It is true that tailwheel aircraft require more precision and control during takeoff and landing. Transitioning to a level-flight attitude during the takeoff roll, and the need to maintain precise heading/drift control during landing, require a little more attention from the taildragger pilot. For a tricycle gear pilot to learn tailwheel technique, he/she needs to fine-tune the ability to maintain directional control at all times. Taildragger pilots call this "using your feet", or "the taildragger tap-dance." The transition from tricycle gear to tailwheel is about as difficult as transitioning from driving an automatic transmission car to driving a standard transmission.
Why build a taildragger?
a) Propeller Clearance -
With a conventional "tractor-propeller" engine configuration, utilizing a tailwheel landing gear arrangement provides a dramatic improvement in propeller clearance. Rough field and off-airport operations can be conducted in a tailwheel aircraft with much less risk of damaging the propeller and/or engine during a ground strike or nosewheel collapse. Debris is also less likely to be drawn up into the propeller of a tailwheel aircraft.
b) Vulnerability-
The Center of Gravity of a stationary tailwheel aircraft is rearward and lower than it would be in a tricycle gear aircraft. This helps prevent "nose-over" accidents, especially when taxiing downwind in gusty conditions.
c) Simplicity - A tailwheel provides significant weight and drag advantages, and is simpler and more affordable to maintain and/or replace.
How do you fly a taildragger?
Once the aircraft is airborne, a taildragger handles no differently than a tricycle gear aircraft. Unfortunately, this can induce a pilot to attempt to force the aircraft into the air prematurely. Typically, a 5 to 10 hour checkout is recommended to master the transition successfully.
The "key" is to master "using your feet" to maintain heading control,
and to master using bank to control drift. A classic "full-stall" three-point
tailwheel landing is very similar to the "soft/rough field" landing technique
taught in tricycle gear aircraft.