"Anecdote for Fathers" has an interesting subtitle ("showing how the art of lying may be taught") that references how this poem explores the ways in which adults can actually make their children lie. This is shown through the various objections that the adult in this poem raises to the child after the child has answered honestly a question posed to him by the adult. When he is pressed for a reason why he prefers Kilve to Liswyn farm, the boy, struggling to come up with a rational reason that will satisfy the adult, picks something tangible that he can point to and says his decision is made because Kilve does not possess a weather-cock. Of course, the poem suggests that this is not the real reason at all, and that the boy has been forced into lying through the need imposed on him by the adult to come up with a rational explanation for his intuitive feeling. Note how this is referenced in the final stanza:
O dearest, dearest boy! my heart
For better lore would seldom yearn,
Could I but teach the hundredth part
Of what from thee I learn.
The speaker recognises that actually the boy in his youth and innocence "knows" far more than the adult, who has lost something as he has aged. Wordsworth suggests that children are somehow more able to be intuitive and responsive to deeply felt inner-feelings rather than closed down to them, as adults are. The speaker in this final stanza recognises that it is actually he who needs to learn from this child, and that the process of education and "teaching" children actually diminishes their capacity to be open to their intuition.
The point is that the child is merely saying that this is the reason he prefers the home in Kilve instead of Liswyn Farm. In reality the child has no particular reason for prefering one place to the other. However, by asking the child so many questions, by providing so many logical alternatives (and we all know that feelings and preferences are not always based on logic) and pushing the child to the point where an answer has to be provided, the child claims his preference is based on something he sees now and does not remember seeing at Kilve. He has based his answer to the question on what is in front of him rather than what he truly feels or remembers. Thus, the "art" of lying has been taught as we teach children to lie by forcing them to answer a question to which there is no definitive answer, by backing them into a corner where there wish to provide an answer (either because they do not want to annoy the adults or just because they are bored of the conversation now).
Hope this is useful
I believe that the poem has two houses, a current one and their old one. Not sure why weathercock is there though.