According to the American Heritage Dictionary definition, Sport is defined as:
Sport \’spørt\ ( Noun )
An activity involving physical exertion and skill that is governed by a set of
rules or customs and often undertaken competitively.
Dance is a physical activity that has rules i.e. keep your turnout, point your toes, etc. In Dance much like many other Sports you must have dedication and time to train and condition your body for the rigors of movement. Training and conditioning involves all 3 components of Physical Fitness ( Cardiovascular Endurance, Flexibility & Stretching and Muscular Strength & Endurance ) and therefore is a Sport that, "involves physical exertion and skill" to accomplish a goal. Leaping and turns are not easily done without skill and technique. Observe and analyze the following photos and consider the power, strength and flexibility it takes to perform these types of movement. Do you believe you could recreate these same kinds of movements safely and accurately? Practice, dedication, physical endurance and conditioning allow these performers to make what is difficult look effortless.
*Dancers above are from the Alvin Ailey American Dance Theater