Close range fighting with a staff is all about leverage and using the staff to pry your attacker off you. I most cases the strike and the leverage work is all the same movement. Once you get your attacker off you, the you can increase distance and continue to hit them with the staff. But you have to know the basics swings for the staff, and you have to use 2 hands. There's now way to create the leverage without the other hand assisting. There's no way to hook the staff around limbs without using 2 hands.
Using only one hand at this range doesn't provide the stability. It would be like trying to sew the end of a flag blowing in the wind with one hand. You only need to about 4 or 5 inches of staff at the end of your grip to create a good hook. The hook that I'm referring too is not the hook of a cane. The hook that I'm referring to is the hook that's is created when you grab the staff.
When we leave a few inches at the end of our grip, it creates a hook. Think of this man's arm as the cane and that small of the stick has the handle / hook. The leverage will come from the larger end of stick. In this picture there's no way for him to create it unless he pulls or pushes on the longer end of the stick. The only way he can do that is to use the other hand.
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When he uses 2 hands, he'll be able to push or pull from either end of the stick. Most times you'll have the opportunity to push and pull at the same time. Being able to slide the hands along the stick would be critical because it's the only way to adjust the hands without fully releasing the stick. This means that two hands are always stabilizing the stick /staff which is great for when there is a lot of heavy contact, like what you'll get when in grappling range. Sliding the hand also allows you adjust the leverage so that it's easier for you to control the staff and harder for your opponent.
Even if a person doesn't have interest in using a stick or staff, it's a fun thing to experience how all of it works.