Whether we like it or not, fathers are authority figures. They set the rules (and can ground us if we don't follow them…), but they can also teach us a lot of things. In "Silence," the speaker's father teaches her (and us, indirectly) how to be a "superior person." Superior people also have authority – by definition, they are higher or better than normal people, right? But in the end, it's the speaker's own choice whether she wants to follow her father's advice and wants to have this kind of superiority.
When the speaker quotes from her father, she is not handing over the poem to him, but rather asserting her own authority. She takes his words and makes them her own, showing that she now has control over when and how her father's words are spoken.