I do actually. We have ballistic missiles. But have we ever tested them on a satellite or a dummy bomber plane flying at high altitude?
Satellite, fighter jets or Bombers are intercepted by SAMs (surface to air missiles) , these missiles have seekers which will track the fast high flying objects and destroy them.
Ballistic missiles till now are meant to destroy the land targets like cities, military installations etc., the missile leaves the earth's atmosphere and then descends on to the target to destroy.
Chinese came up with the idea of destroying carrier battle groups with BM's since using BMs against large flotilla has its advantages. There are various guidance systems which are used in BMs and since the carrier battle groups will not travel that fast( Max as per specifications 30 knots) BMs can be used to destroy carrier battle groups, with bigger pay loads.