We get hit on the head with "silence" as a theme as soon as we read the title, but the poem itself gives us a bit more than promised. The poem constantly negotiates between silence and speech: who gets to talk and who has to stay quiet, what is said and what is held back, should we read the text literally or should we read what the text implies, etc. The ambiguity we see in several lines also makes us wonder: can a lot of words really tell us nothing, while silence can tell us everything?
The speaker lets her father do most of the talking in order to demonstrate her restraint. She shows us that she could be talking, but deliberately withholds her own opinion.
The father's long quote shows that he doesn't follow his own advice. He values silence, but he talks through most of the poem. The speaker quotes her father to cast him in an ironic light, not because she agrees with his opinion.