Well, to make it simple, for a muscle to grow in size and strength you must continually increase the resistance to which it is being subjected to. Muscles are made up of a shitload of muscle fibers consisting of muscle cells. When a muscle lifts a weight the muscle fibers contract and the muscle cells either contract or don't contract at all, it is important (if you are trying to build muscle) to make sure to use maximum weight combined with strict form to ensure all the muscle cells are contract. If you always trained at the same weight, your muscles would plateau, and you would not see anymore growth.
Ok, after reading that....now consider that while doing a pushup you are only lifting about 40-45% of your actual bodyweight... well... to put it bluntly, that aint gonna do shit for your muscles nor strength
.