More like, it's the fact that you're using them in a defensive formation. But there are numerous ways to smash that formation in EB, the easiest method being to gang archers and/or slingers on you, shooting over your line and hitting the backs of those on the other end, or into the flank of those perpendicular to the line of approach. Or one could sacrifice a high-morale elite unit to push in between your phalanxes and into your square to wedge open your phalanx. As long as I focus my attack on the boundary of units and punch my way through there with spearmen and my family member nearby, I can break you, and possibly your family member too, though it will be bloody.

That, and the enemy was using a traditionally defensive formation in attack. Incidentally, that was the problem with the Successor states' tactics. So nope, it's not that your Chalkaspides are invincible. Just try attacking with them and you will realise the same thing you could take advantage of with the enemy will apply painfully so to you. Of course you will win, but you'll still lose men.