I believe that in order to increase the size of a muscle you have to increase its strength (and I am certainly not alone in believing this). The two go together (for a given individual, that is). For a host of reasons one guy with slightly smaller muscles may be stronger than another guy with slightly bigger muscles but any given individual will become stronger than he was before if he increases his muscle size and vica versa.
To increase the strength of a muscle you need to be lifting at least around 70% of your maximum possible for that muscle.
Low reps (generally 6-8 and sometimes even 3-4, in any case no more than about 10 reps) with heavy weights is what builds big muscles not a high number of reps with light weight. (High reps with light weight will improve your endurance - by increasing cardiovascular efficiency and may also be beneficial for weight loss - so it is not without value, still it is not how to build massive muscles).
The problem with push ups is that you aren't lifting that heavy a weight when doing a push up (thats why you can do 50 or even 100 of them). When you do a push up you aren't even lifting your own body weight but rather about 60% of it, the other 40% is supported by your feet. (Get in the push-up position on a pair of scales to see just how much percent of your mass is being supported by your arms, unless you're very top heavy it won't be more than about 60%).
So if you weigh say 150lb, doing a pushup will be roughly similar to doing a 90lb bench press. Now for a beginner an 90lb bench press may indeed be heavy enough to stimulate muscle development (because it may be within about 70% of his maximum strength) and so he may indeed find it a descent exercise which will lead him to see an improvement in musclularity.
However most people can with training bench at least their own body weight and so the 150lb individual will (if he trains right) eventually be able to bench 150lb and then 200lb and maybe even eventually 300lb. Once he's benching more than about 130lb our 150lb guy will no longer find benching 90lb (or doing push ups) to have any benefit in increasing muscle size or strength.
The bottom line is that most people within a year or two (if not a couple of months) develop their muscles to a point where push ups simply are of no more benfit in regard to increasing muscle size or strength.
Now of course a guy who starts out body building weighing 150lb will increase his weight (maybe to 200lb after a couple of years) and hence be lifting more when he does a push up. Never the less he will still never be lifting more than about 60% (and certainly never more than 100%) of his body weight and so still won't find push ups usefull for increasing muscle mass (beyond a certain point).
That is to keep increasing muscle size and strength you need to keep increasing weight lifted/benched and as push ups do not allow you to do this there is a limit to how strong pushups by themselves will allow you to get.
