text: There is more to the system than just the man and the wall.  Let's say the wall and man are hovering in space and they push against each other.  They would separate resulting in motion of both man and wall.  \n\nBut on earth, when a man pushes against the wall and visa versa, they are both anchored to the ground.  As the man pushes the wall, the wall would move but the earth is pushing on the wall the opposite direction.  Likewise, as the wall pushes the man, the earth pushes him in the opposite direction through his feet.  This can be illustrated by supposing the man were on ice and had no traction.  He would surely glide away from the wall.  \n\nSo how can there be force with no acceleration?  Let's take the man's perspective.  He is pushing on the wall resulting in a force the opposite direction, but he is also experiencing the earth pushing him towards the wall.  Since both forces are equal and in opposite directions, the man's net force is zero.  The same goes for the wall.  \n\nSo, while your question is technically correct, you didn't take in account that there is more than one force involved, and those two cancel each other out.