Aside from the "We live society" jokes...
Hanging yourself like that is an exceptionally bad idea.
The goal is to snap your own neck by kicking the chair so fast that the sudden force breaks. If you try to just sit there and have gravity crush your windpipe or suffocate yourself out, it could take minutes, if not hours, in which you are struggling and instinctively fighting for your life, even if you want to die as self-preservation kicks in. It's so painful that it's not uncommon for you to grind your own tongue off, and you violently end up flailing helplessly.
It's no wonder why he cut the rope then.