Why does a matchstick not burn on its own?
This is because for anything to burn , there is need of certain minimum temperature called its ignition temperature.
Ignition temperature of the matchstick head is about 230oC , but the temperature of room is hardly equal to 20-30oC ,so the temperature of room can never be equal to the ignition temperature of matchstick and hence it does not burn on its own.
Match stick does not burn on its own because temperature is less than the ignition temperature. On stricking with the walls of match box, sufficient amount of heat is produced due to friction which raises the ignition temperature of the chemicals on the match stick and thus burns.