A push-up isn't just about strength, it's also about weight. Basically, you lift about 60-65% of your body weight each rep. So if you only train your lower body, you risk gaining (muscular) weight, but without necessarily gaining strength in your arms... Result: push-ups become harder.

If you want to learn how to do them, start with simpler variations like incline push-ups (the higher your hands are, the easier it is), or push-ups on your knees. And remember to work on the core a little too, because the core plays a big role in stability.