Remember the time when you bro-fisted your friend, and also the time when you used to draw a watch in your wrist. So what is alike? Well, in both the scenario, your skin was 'touched'. Your hand touched your friend's, and your wrist touched the pen, but did it? Technically, no. What if I say you that all the handshakes you did, was done without touching the others. Bamboozled, aren't you?
What are we made of? Atoms, to be precise. And what makes an atom? Electron, proton and neutron. And Rutherford discovered that atom is 99.999999999999% empty. Perhaps, the distance between the valence electron and nucleus is greater than you can imagine. The electrons possess negative charge and protons possess positive charge. So, Physics 101: they create an electrostatic field around them. Thus, negative and positive charge attracts and same charges repel each other. Now recall the fourth sentence. Thence, when two atoms approach each other, they first meet each other's electron cloud first, and you know what happens next: REPULSION!
Congratulations buddy, you have been levitating all these years! Even right now, you are floating on your bum. All the 'touches' that you do are just the consequences of repulsion. Every time you cut paper with scissors, refusal between the electrons makes the paper tear. Next time your cousin accuses you of 'touching' his/her cake, be sure to clarify that you are not the one to blame. Moreover, you have never touched anyone in your life and you are going through existential crisis all your life.
But why does it 'feel' different when you are hit with a stick, and caressed by your parents? Basically the mystery lies within our body. Human body is sacked with nerves inside out, and different nerves behaves differently. Also objects with different structure, density, state of matter, force, etc. create different types of repulsion, and those repulsions stimulates our nerves. Ultimately our brain/spinal cord identifies whether it is hit on your skin or a kiss on your cheek.
The only time your body touches something is when it undergoes chemical reaction with anything. The digestion process, reaction in haemoglobin, and whatnot. Not only for human body, it holds true for other substances too. So does it literally mean that we have never touched anyone in our life? Since I am not a post doctorate professor of biology, and I am a computer student, I cannot explain the biological secrets, perhaps the procedure of DNA formation. Intuitively, the closest that we can get is with our biological parents, and our children. Perhaps, loving and respecting them should be your priority since they are literally your 'closest' one.