Here is a strategy to work towards your first strict push-up.
It sounds counter-intuitive, but weighted push-ups can help you get that first strict push-up. The body can handle much more load during the eccentric, or lowering portion of movement. See pictures below.
The Eccentric Phase:
This is beneficial because the majority of muscle breakdown, which causes growth happens during the eccentric phase. Basically more stress on the muscle = more muscle (as long as you recover effectively). Adding load is easy, just place something with weight on your back. Obviously a barbell plate is optimal because it is easy to balance and you can easily track the weight used. If you are doing this at home, get creative, you can use a phone or text book, a bag of potatoes, or have someone push down while you resist.
Under Load:
To come up, simply reduce the load before pushing up by removing weight off of your back or coming up from the knees. By doing weighted push-ups, you also get the added benefit of core strengthening since you will be holding yourself in a plank position throughout the movement. Just make sure to keep the core tight!
Now drop down and give me 20!
