I would mostly justify this statement with an examination of the complexity of family relationships, particularly between parents and children. As is so true today, parents and children don't often communicate well. They misuse and misunderstand each other. As the children get older, they take leadership roles in the family that can cause the parent to end up in a position of inferiority - role reversal. A dutiful child is often not respected by the parent, who may take them for granted or misunderstand their actions. If parents and children weren't still fighting so much, there'd be a huge decrease in the number of psychologists needed!
Because of the sweeping nature of its themes, many critics would agree with this statement. Some compare the play to "Cinderella" for the relationship it depicts among the sisters; others point to the need of the father for the unconditional and vocal love of the daughters as a means to assert an otherwise fading power in the context of aging. The senseless of the universe as a theme--that it really does not care and has no rhyme or reason for its actions -- becomes particularly relevant in our century. This theme emerges out of the context of deep loyalty that Lear's friends and daughter show for him, to be sure, but Cordelia's death at the end seems unjust, and it is with that injustice that the play ends.