I do not know how it is explained inside the universe, but I suppose it is handwavium as almost all superhero stories which do not make any sense in reality.
You are right, it does not work. Even if Ant-Man is extremely strong, he is almost completely harmless for a human because he could move his extremities only in the millimeter range which is fully in the range of human skin elasticity. If I stomp on him, he will be able to stop it and I recognize that something stopped my foot, but if he throws the foot up, the foot will be accelerated only a few millimeters which does not make any effect. He can crawl on me; if he punches, the skin gives way, so the best he can accomplish is a small bruise; he is not even able to get to the bones. Remember, too, that he needs a pivot: If he punches, he is accelerating himself, so he would also only propel himself away from the human. He may try to tear on the skin, but the skin is elastic enough to be stretched a few mm without harm. He may be able to pull hair out, but this is only painful, not incapaciting. The only real damage he could do would be inside the body (eardrum !).
It is also a wrong contention that ants are very strong. It is the good old Square-Cube Law in action: A human who shrinks loses weight much faster than strength, so an ant sized man would be in fact able to jump higher than a flea and kill any ant without problem.