Torque and Equilibrium
We said that for a system to remain in static equilibrium, the horizontal forces must balance— the total force pointing left must equal the total force pointing right— and the same must be true for the vertical forces. Now we must add a third condition: that the torques on the object must balance as well. When an object can spin in a circle (like a door), then torques can be divided into two categories: those which tend to make the object spin counterclockwise, and torques which tend to make the object spin clockwise. Static equilibrium requires that these two must balance.When an object is spinning around a particular point, like a wheel around an axle, then it's obvious where to put the pivot. But if an object is not spinning, then it's not spinning around any point. In this case, the "pivot" isn't a physical object so much as a mathematical choice: we can place our "pivot" anywhere we want, and so long as the torques balance around that pivot, they will balance around any pivot.
Sometimes a clever choice of pivot can make a problem easier to solve, or allow you to see the problem in a different way.
But if the pivot is on the right, then the blue force exerts zero torque, but the red and purple forces both exert counterclockwise torque. There is no way the torques can balance in this picture, and so the ruler cannot be in static equilibrium in either picture.
Remember that the "pivot" isn't a physical object here; it's just a mathematical tool.