This program ISN'T designed to get you to 100.
This program is TITLED 100 pushups, because that's good marketing. But the program itself is, to put it kindly, seriously flawed. The jumps on weeks 3 and 5 aren't reasonable. Are you really supposed to believe that hitting a 25 rep max in your week 2 test, means you're ready for a four-set pounding in week three where the FIRST set is 25? And then, you have to do at least 25 AGAIN, on your 4th (?!) set to move forward? And week 3 isn't half as bad in this respect as week 5.
The way to push your body's limits forward, when you're dealing with bodyweight exercises, is like this:
First, do enough reps of the exercise that you push your body to and beyond its limits. (Actually, you only CAN push your body to its limits. But "to and beyond" gives a better idea of exactly what it means to hit those limits for real.).
Second, rest. Thoroughly.
Third, repeat.
The program linked is guaranteed to lead to overtraining and less-than-optimal results. Particularly if the result you're after is getting to a rep target in a hurry.
Anyone wants a real program designed to get them to 100 pushups ASAP?
Day 1 - Do about 20 wall pushups, standing, just to get blood flowing to the muscles. Alternatively, jog in place, or cycle for 10 minutes.
Then do pushups. One set, to failure. Not till it becomes uncomfortable. Till your arms give out. Till you push with every last ounce of energy you have, and still can't force your body upwards. End of workout.
Day 2 - Rest.
Day 3 - Rest.
Day 4 - Repeat day one till set >= 100.
If you don't improve your max every time out, add another day of rest. You'll get there a hell of a lot faster than you would on the prescribed program.