Fad diets are not recommended because

Following a fad diet restricts a person from a specific food or food groups. Doing this will only make you want those food even more. It can also make someone hungrier, in which they will break their diet and binge eat due to the low amount of food intake. This can reduce metabolism and make one lose their progress. Fad diets are prone to failure.

Push up require upper body strength, so weight-training exercises such as shoulder press, curl ups and dead lifts would improve your ability to perform proper push ups.