we never touch anything!

The sensation of touch is actually a big illusion, as proved by physics.
Let's talk simple.

Every atom, as you may know, contains a nucleus which occupies 1% of the total volume of the atom. The remaining 99% is empty. It is in this empty space, that we find electrons revolving around the nucleus.

Now the basic property of any charged particle is that it repels a similar charge. The force of repulsion grows stronger and stronger as the two charges get closer. This is in accordance to the inverse square dependence of force with distance - d.

Now if ‘d’ is reduced to zero, the force will become infinite, which is not possible.
This is why, two atoms, two surfaces can never come in pure contact with each other. There will always be an infinitesimally small distance in between them, even if it is as small as 0.000000001cm