I always take the advice of "push through the pain" as pushing through the pain of exhaustion, which will contribute to strength and your ability to push beyond current physical limits; whereas the advice of "listen to your body and stop when it hurts" is more related to injuries - if you have a constant muscle cramp, or joint pain, or a stress fracture, or a ligament issues... REST and recuperate. Pushing through this second sort of pain will very likely result in injuries worsening and requiring even longer to mend down the road.