Things don't fall through other things because they are levitating on an electrostatic field! I am not kidding! When you sit on a chair, you are not really touching it. You see, every atom is surrounded by a shell of electrons.
This electron cloud presents a rather negative face to the world. Remember that like charges repel each other. When two atoms approach each other, their electron shells push back at each other, despite the fact that each atom's net charge is 0. This is a very useful feature of nature. It makes our lives a lot easier.   _{Your Comment}