There're many doors that don't have a handle or knob that needs to be twisted to open them. These are usually in public buildings. You either push or pull to open the door. Why do other doors have knobs or handles that must be turned to open them? Is it just to prevent a person who leans against an outward-opening door from falling over and getting hurt?
All doors need a mechanism to keep it closed. Otherwise it will be opened by wind, air pressure changes, vibrations, animals, kids, leaning, and so on. The door knob or handle is just a mechanism to open it up.
If left out, like in the "public building door" for reasons Ivan Venediktov explains in his answer, then that door needs some other mechanism to keep the door shut. For example, a spring arm mounted on top that closes it automatically, or a spring catch and counter-piece, replacing the one being turned by a door knob, that keeps the door shut until you push or pull enough.
The other mechanisms are just not always convenient everywhere. For example you don't always want a house door or an apartment door to close automatically. And you might not want your toddlers, pets or wind to be able to open the door without you noticing. The force applied needed to open or close might be different for different people, and harder to maintain, and price for a spring arm is higher.
The manually control door knob is just more simple and controllable.
One of the reasons in that the animals can not easily operate a door knob. I never came across any exact information on "why door knobs exist", but it is the only thing that comes to my mind.
It is more practical however to use pull doors in public places (ex. shops, cinemas etc.) as any door handle will get broken within a couple of days dues to the heavy duty.
And you should also read this: Why do door knobs still exist?