Bodyweight Exercise is a Great Body Fat Tester
It's easy to think you're getting stronger if your lifts are going up, even if your waistline is expanding right along with them.
Increasing your body mass can improve your leverage to lift an external load, regardless of whether that mass is comprised of fat or muscle. With calisthenics training, however, any superfluous body weight you're carrying will decrease your leverage and make your exercises more difficult by creating additional resistance.
In other words, if your body fat percentage is greater than your max number of push-ups, you have a low strength to mass ratio, which is basically a more scientific way of saying that you're too fat. If this is the case for you, the only pie you should be eating is a big ol' slice of humble pie.
Put your ego aside and devote yourself to improving the basics. It doesn't matter how much you can deadlift; if you can't do a single pull-up, you're not strong.