This is part of the (usual) definition of DFA. It is difficult to argue with a definition.
While it is difficult to argue with a definition, one may wonder why the object was defined in a certain way. Here an answer is that we want our automaton to be always in a particular state, no matter what happens. In other words, we want the transition function to be a function instead of just a partial function. It's a matter of taste.
Some people allow the transition function to be partial, and they still call the resulting model DFA, although this is probably less common than Sipser's definition. The two definitions are almost equivalent: accommodating a partial transition function takes at most an additional state of "subsidence".