Please consider two cases.
1)Suppose a rod is hinged, such that it is free to rotate about one of its edges. Now, the rod rotates with an angular acceleration α under the influence of a force F applied on the other end. We can find out α easily with the torque equation (Given that mass & length of rod is m & L). Now in this condition, if we apply torque equation on the COM of the rod, the angular acceleration that we have here is same.
Note: $F_1$ & $F_2$ are the forces provided by the hinges.
Why is the angular acceleration different? Doesn’t it has to be the same?