You know how some people are really nice, but you just know that you'll never stay up all night with them, eating pizza and gossip about ex-boyfriends/girlfriends? Between the speaker, her father, and the superior people he describes, this poem feels like a Not Going to Be Your New Best Friend Club. All these people, in their own ways, keep a distance between themselves and others.
In this poem, we really get two speakers: the person saying the poem and the father, who provides the quote. Even though the father praises people who enjoy solitude, the poem itself is a rejection of solitude.
The father's use of the cat to illustrate self-reliance is flawed, because the cat, as much as he may enjoy his privacy, relies on the mouse to be his prey.