The whole point of this poem is to convince a young man to have kids. The speaker argues that by having a son, the young man will create a family line, and his beauty will live on. But that's not exactly a family, is it? Be sure to notice that this poem doesn't say anything about a wife, or the possibility of him having a daughter. That's weird, because it's tricky to have a kid without a woman being involved somewhere. We think this might have something to do with the relationship between the speaker and the young man. (Check out the theme "Appearances" for more on this topic.)
Because this poem is meant to appeal to a young man, it purposefully leaves out the idea of marriage and the traditional notion of a family. The speaker is attempting to describe the benefits of family without mentioning the responsibilities that go along with them.