Simon, the clapper box hinge ie pivot pin, performs two functions :
1 It allows the cutting tool to be loosely dragged back along the work piece surface to avoid wear of the cutting tool tip, as per John W.
2 It supports the lateral force exerted from the cutting tool, hence, that is why it is screwed down tightly.
The up/down movement of the cutting tool is controlled by the adjustment screw, see pic, it should be adjusted and locked to give, say 0.025 mm (0.001 inch) clearance, more than one adjustment screw can be fitted if necessary.
The shape of spline, gear etc. cutting tools are normally equal about their centre line and so once the tool has entered the work piece the up/down forces are also equal, therefore, the tool tends to stay in a straight line.
Regarding the use of HSS or carbide, it has been my experience that when intermittent cutting ie turning, slotting, broaching etc, HSS is preferred as it has more "flexibility" than carbide and is therefore less likely to fracture.
At one time I was involved in the design and manufacture of broaches used to cut the firtree slots in aero engine turbine discs that hold the blades, those broaches were always made of HSS for the same reason.
Well, thats my ramble over, shan't now have to go for that walk today