# Why Benders cuts are valid?

In Benders decomposition algorithm, we first solve a master problem which provides us with a solution vector. We then use this vector to construct a subproblem. For a minimization problem, subproblems give an upper bound (since it is a restricted version of the original problem). If the upper bound is strictly greater than the lower bound (provided by master problem, a relaxation of the original problem) then we add a Benders cut to remove this point (i.e., the solution vector obtained from master problem).

I understand why this Benders (optimality) cut is used to remove such point from master problem, but I don't understand why it is valid. In other words, this point is not the only point which is removed from the feasible region of master problem when this cut is added. Can someone explain the rationale behind this in simple terms? On the other hand, there might be many more cuts that can remove this point. Why among those cuts we can (usually) only prove that Benders cuts are valid?