To achieve full power of a punch, it is essential that both arm cooperate, that is usual what you will hear in the Dojo. One arm (fist) is thrown out, while the other arm is pulled in to the side of the body (Hikite). Both arms perform the same movement, understood in the sense that, if the right arm comes out in a straight line, then the left must be retracted in a straight line. If the movement is circular to the right then it is also circular to the left.
But !!!! You will often hear that Hikite is for generating a powerful punch only. However, this is not quite right. Hikite is much more than just a hand pulled back to the side of the body for generating a powerful punch.
If somebody attacks you, it will be normal to take up your arms to protect yourself; it is a question of reflex.
I think that Hikite function already starts here. Hikite first task is to block (reflex). If possible, you will grab the opponents arm (or something else) and pull back, that is the use of Hikite. The opposite arm (fist) is offensive and attacks.
Hikite is not just for block and grab. It also acts as a control arm where you try to control the opponent’s arm and movements.