I think that one of the reasons why some people don't understand why they can get strong with Bodyweight-based strength training is because they are familiar with only one way of getting strong: Adding weight to their body. This works by increasing the gravitational pull on their body and forcing the muscles to contract harder. Obviously, there isn't a strength training method proven build muscle than weight training. That doesn't mean that other ways don't work at all.
Calisthenics work by using a combination of your body's weight (and gravitational pull) and decreasing your leverage during the movement. Now, as you get better and do more reps, the solution to making the exercise doesn't have to be adding more weight. You could change the height of certain body parts and add weight. For example, if push-ups are getting too easy, simply put your feet on a chair. Plus, it changes the leverage. Now you'll have to use your serratus muscles more on the movement.
Then there's always adding instability to the movement. Instead of putting your feet on a chair, you could put them on a basketball. Or, if you had two balls, do push-ups with your hands on each ball. Dip down low between the balls too. That will complicate things.
Or, you could eliminate the movement all together and do an isometric hold. That isn't as easy as it sounds. If it is, refer back to the previous paragraph and do it on an unstable footing. You could hold this position for a minute or your could tense your muscles as hard as you can and hold the contraction for 10 seconds while exhaling.
Then you could add other moves to the push-up. You could do a plyometric clapping push-up. If that's too much then you could do an alligator push-up, bringing your knee to your elbow. Have you ever heard of 8 count bodybuilders or burpees?
Now, some of this information may be repetetive but just remember that there are more ways to get strong than just by weight lifting. Sure, gyms are great to go to but I've seen too many people's quest for fitness get screwed up because they were dependant on the gym in order to get in shape. Then I've seen people use not being able to get to a gym as an exuse for getting out of going.
This is why I think that BW training has its advantages over weight-based strength training. You're not dependant on much of anything or a specific place. You've always got the ability to work out, no matter what setting that you're in. You've got the means so you never have an exuse. It's the most verastile strength training methodology out there. That's why I'm such a big fan of it.