Why does the chest muscle ache after doing push-ups?

You're right. The point is that every time you do push-ups, your attention is highly focused on your chest. (In fitness, this is called nurturing ability.)

So when you do push-ups, compared with when you do bench press, push-ups stimulate the chest muscles more and the training is more in place, so you say that bench press is not strong on the chest muscles.

So next time you can try bench press to improve your chest muscles and make your chest better stimulated.

As for what you said, the chest will be particularly sour the next day. Because after every training session. Muscle will form lactic acid accumulation

Extended data:

Lactic acid is an intermediate product produced in the process of glucose metabolism during exercise. Due to relatively excessive exercise, which exceeds the intensity of aerobic exercise, lactic acid produced in the body cannot be further decomposed into water and carbon dioxide in a short time, and insufficient oxygen supply forms anaerobic metabolism, resulting in a large amount of excessive accumulation of lactic acid in the body. Lactic acid accumulation can cause local muscle soreness.

So it's okay, and then about chest training, do the next training every 48 hours, because the recovery time of chest is 48 hours.

Finally, you said you relaxed your muscles and stretched them.

You can try a new stretching method.