Playing a kobold Champion (LG of Kurgess) with the cavalier archtype, mounted on a mature riding drake, armed a blade ally infused lance. My opponent is a goblin on a warg with a horsechopper. We noticed that, in the RAW, I am unable to hit the goblin with my lance due to being on a large mount, but the goblin can hit me with his horsechopper as long as there is a single space between us.
Is this correct or did we miss some rule that makes the mounted combat rules make sense?
It doesn't mean that, fortunately. Your assumption is correct.
You occupy every square of your mount’s space for the purpose of making your attacks. If you were Medium and on a Large mount, you could attack a creature on one side of your mount, then attack on the opposite side with your next action. If you have a longer reach, the distance depends partly on the size of your mount. On a Medium or smaller mount, use your normal reach. On a Large or Huge mount, you can attack any square adjacent to the mount if you have 5- or 10-foot reach, or any square within 10 feet of the mount (including diagonally) if you have 15-foot reach.