When we exert a force of X N on a box in contact with another identical box on a frictionless surface, the resultant force on both boxes is 0.5X N. My question is, why doesn't the first box push the second box with the entire force of X N, instead of pushing it with only 0.5X N? I realise that this would mean that the first box shouldn't move at all, because according to Newton's 3rd law, the 2nd box would push the 1st box with an equal and opposite force of X N and thus the resultant force on the 1st box would be 0 N. But I don't understand why it is necessary that the 1st box HAS to move.
The force applied on second box is by contact. Therefore in order to constantly apply the force on second box, first box has to move to stay in contact. Half of the force is used up in accelerating the first box.