In cutting down a tree, a logger makes a cut on the side facing the direction in which the tree is to fall. Explain why. Would it be safe to stand directly behind the tree on the opposite side of the fall?

The side on which the cut is made is no longer supported by the normal force from the bottom, therefore, the gravitational force acts on the tree and tries to rotate it. The torque provided by the gravity will rotate the tree such that the tree falls on the side as anticipated by the logger.
At times, it is not safe to stand on the opposite side too. The tree can rotate the other way depending on certain others factors such as the direction of wind and the precision of cut.