Even if we accept the need for static typing, object-oriented languages introduce a new twist into the static/dynamic typing distinction.
The is-a relationship asserts that an instance of a child class is in all important respects a representative of the parent class. Thus, the value of a child class should be able to be used where we expect a parent class.
This means that a variable declared as one type, say Mammal, should be able to hold a value derived from a subtype, such as Dog.