The term catharsis comes from Greek tragedy. Since these plays deal with a king or prince or someone from a high position who through hubris (usually) falls from that high position. The fear comes from the idea that if a person from such a lofty position can fall what about the common man? The pity comes from the idea that we feel pity for these tragic heroes who aren't bad people but ones who through their own humanness suffer and in some cases die.
In the case of King Lear, his vanity keeps him from hearing the truth. When he asks his daughters how much they love him, he provers that he does not understand love itself. His two eldest daughters play daddy's game and give him the answer he wants. Cordelia, however, tells him the truth.
Lear's mistake is to think that we have so much love and must divide it among those we love. He fails to recognize that love is expansive, not reductive.
In his fit of temper and hurt pride, he not only banishes his favorite daughter but also Kent who also dares to tell him the truth. Of course, the Fool tells him the truth also but he is a fool, so Lear doesn't really listen to him. The result of this pride leads Lear to madness.
It is frightening and sad to see this king decline and descend into madness. It is even harder to watch as he realizes too late what love is.