Being unstable in the ground is one of the disadvantages of conventional landing gear (aka taildragger) aircraft. They are susceptible to Ground Looping.
From Wikipedia:
Conventional geared aircraft are much more susceptible to ground looping. A ground loop occurs when directional control is lost on the ground and the tail of the aircraft passes the nose, swapping ends, in some cases completing a full circle. This event can result in damage to the aircraft’s undercarriage, tires, wingtips, propeller and engine. Ground-looping occurs because, whereas a nosewheel aircraft is steered from ahead of the center of gravity, a taildragger is steered from behind (much like driving a car backwards at high speed), so that on the ground a taildragger is inherently unstable, whereas a nosewheel aircraft will self-center if it swerves on landing. In addition, some tailwheel aircraft must transition from using the rudder to steer to using the tailwheel while passing through a speed range when neither is wholly effective due to the nose high angle of the aircraft and lack of airflow over the rudder. Avoiding ground loops requires more pilot training and skill.