Mothers always pass down an X chromosome to their children (both male and female). However, Fathers can pass down either an X chromosome or a Y chromosome, which determines the genetic sex of the child.
When a father passes on a Y chromosome, the child is genetically male because they have a mixed set of chromosomes, XY: the X chromosome from their mother and a Y chromosome from their father.
When the father passes on an X chromosome, the child is genetically female because they have a pair of X chromosomes: one X chromosome from their mother and one X chromosome from their father.
Therefore, since genetic females do not inherit a Y chromosome, they can not take a Y-DNA (paternal lineage) test.