In a skit ( a comic play or a drama), everyone is lively and playful.
skittish=skirtish: think of girls all with short skirts showing skirtish (skittish) behavour,
when u r walking on skates (skatish), u r very lively and playful
SKI is a long strip of wood fastened to the foot for sliding....hence SKITTISH people are lively, playful...
skits are subjected to change pretty easily
Rhymes with "citish", as in "citish life" - changing, lively
everyone feels skittish(nervous) during skating.