When squatting positively, i.e. when you push yourself upwards from a parallel position, should your arms be used to push the barbell to assist the squat?
Absolutely not. You should be pulling your arms down, and your shoulder blades together.
The idea is akin to “lifting yourself up by the bootsraps.” Unless the weight is light enough to actually push-press your legs are going to be doing all of the work no matter what.
If anything (vector rant incoming) the weight from the bar is going to make the squat harder if you try to push with your arm because although it may seem you’re applying extra force it has to come from the ground. Now if you have 200lbs already sitting on your back and you try to push with your arms AND legs it’s going to create extra force on your body. That’s why most people automatically pull down on the bar on hard reps. The human body is smarter than we are sometimes