Why does applying force to a rod in space (or any other isolated systems) on one end leads to both translational and rotational motion?
Here's my logic: suppose there is a rod in space. We magically apply force on one end, perpendicular to the rod. From Newton's second law of motion: $$F_y=ma_{cm,y}.$$ The only force acting in the $y$-direction is $F$, so $a_{cm}$ must equal to $F/m$. Consequently, the rod purely translates as a whole and it doesn't rotates. There is no net external torque because the end of the rod is accelerating linearly along with the center of mass.
The answers to this related Phys.SE question assumes that there is torque, which I can't see why there should be.