Describe the theme of parent-child relationships in King Lear.
It's notable that in the various parent-child relationships presented in King Lear, it's the children who display greater maturity than their parents. The most obvious example, of course, would be Lear's daughters. Regan and Goneril understand immediately the full import of their father's foolish decision to divide his kingdom between them and their sister Cordelia. They know that as soon as Lear gives up his kingdom, his power and authority will start draining away.
For her part, Cordelia shows a rather different kind of maturity. In refusing to make a public profession of love for her father, she's effectively telling everyone that she'll have nothing to do with such a silly, childish charade. No longer daddy's little girl, Cordelia is now very much a woman in her own right.
Then there is the immaturity of Gloucester, so easily seduced by the lies and deceit of Edmund, who expertly turns him against his legitimate son, Edgar. As with Lear, Gloucester is so childishly insecure that he desperately needs to feel the love, and Edmund is only too willing, for purely ulterior motives, to make him feel it—just as Regan and Goneril professed their love for Lear to get their greedy hands on his kingdom.
King Lear and his daughters are, of course, a completely dysfunctional family. Lear himself (at the play's beginning) is a narcissist who demands submission and utter devotion to him alone as evidence of his children's love. But he is so self-involved he doesn't recognize he's raised two sociopaths in his older daughters, Regan and Goneril ("the pelican daughters," so-called because the Elizabethans believed that pelican chicks fed off blood drawn from the chests of their parents) until it's far too late. These two lie through their teeth to get what they want from him—parts of his kingdom and the power that goes with it. On whom did they model this behavior? Without doubt, their father.
Cordelia, on the other hand, while genuinely loving her father, refuses to say she will love only him, and is reviled for it. It's only when she and Lear (now dethroned, crazed and at the end of his life) are reunited at the end of the play that he recognizes her worth: again, too late.
The theme of parent-child relations is so important to the meaning of King Lear that one could write a book about it. To name the heart of it, though, Lear shows that he misunderstands the way in which a daughter's love to her father should /must be expressed, and fundamentally misjudges Regan and Goneril, taking their flattery at face value. However, if he misjudges those two, his judgment of Cordelia is something close to a crime. He so underestimates her love that he blasts her in the opening act.
The rest of the play then dramatizes what happens when these relationships go bad, with Cordelia embodying what a daughter should be and do for her father.