How does the parent and child relationship bring about King Lear's tragic outcome?

Lear has a superficial understanding of parent-child relationships—or rather, what constitutes a healthy parent-child relationship. He eats up the flattering words of Goneril and Reagan, not noticing the lack of true feeling behind them. Neither love their father, but their showy displays of affection seem to be enough for Lear. Cordelia is upfront and honest, not willing to play the same game as her sisters. While her words might seem unnecessarily harsh, she is only being truthful. Yet she is the only daughter that truly cares about her father. Unfortunately, Lear cannot see this and rejects her, feeling she isn't worthy of his love.
Lear gets a rude awakening when his older daughters no longer obey him or seek to please him. Now that he is at their mercy, they show him none. Lear's inherent belief that children owe their father blind allegiance is shattered. This leads Lear to the edge of madness. He does get to reconcile with Cordelia, but by then, it is too late for them to have a happy ending. Cordelia is murdered and Lear dies brokenhearted, unable to go on without the one child that loved him for who he was and not because of his former power as the king.

King Lear mistakenly believes the words of love that his two older daughters, Goneril and Regan, lavish on him when he is about to divide up his kingdom and retire. Lear's first great error is to credit words more than deeds. He trusts the two daughters who lie to him and banishes the one daughter who truly loves him but will not flatter him. 
Beyond that, Lear trusts in the parent-child relationship. He is so used to being obeyed and (seemingly) respected that it does not occur to him that his own children could betray him after assuring him of their love. He seems to lack any radar to detect being conned by a daughter. He does not understand that the parent-child relationship is based on power, fear, and love. He also does not understand that some children only desire their parent's wealth and power, rather than their parent's love. Lear is stunned and shattered when Goneril and Regan betray him and use the power he has given them against him.