A list of ancestors is chance piled on chance. But the mind cannot rest in that, so the names are sorted into three equal groups, as if time kept a steady beat. This ordering is the old wish to feel that the past was going somewhere.
The three groups also carry a familiar story: a rise to greatness under David, a fall into darkness and captivity in Babylon, and a return that ends in a new birth. People live those same three seasons, rising, sinking, then returning changed. Sorting the generations this way makes the child feel less like an accident than the point the whole line had been moving toward.