Bodyweight movements can be the most annoying. You're moving your body through space, this part is supposed to bend while this part is supposed to stay straight. This needs to stay tight, while this muscle has to relax for movement to happen. Then there is scaling. You weigh what you weigh, and you can do modifications, but we all crave the full movement.
Two articles on the push-up, first from the Huffington Post that talks a bit to back sagging:
Huffington Post: Perfect your Push-up
Now a video from KStar's Mobility WOD which talks a bit more about core stability in the push-up, why we don't much like knee push-ups, and proper arm placements. Also, check out this slingshot action:
Mobility WOD: Push-ups and Sling Shots