When Lear first speaks, he seems like a logical and generous king. He wants to divide his kingdom three ways and give the portions to each of his daughters. He realizes he is getting old and feels that the time is right to confer his kingdom to his daughters ("younger strengths") giving him time to relax/retire. However, he soon proves that although he is generously giving away his kingdom, he is proud; he expects each daughter to profess her love for him so that "we our largest bounty may extend." She who professes love for Lear most eloquently would apparently get a greater share of the kingdom.
Goneril and Regan make passionate speeches. Cordelia decides to say nothing superfluous. She does this to be true.
Unhappy that I am, I cannot heave
My heart into my mouth. I love your majesty
According to my bond, no more nor less. (I.i.89-91)
Lear is so proud that he just can't see the logic and truth in what Cordelia is saying. Lear wants her to top her sisters' proclamations of love, but Cordelia won't make a mockery of her true feelings. Not only does Lear refuse to give Cordelia a portion of his kingdom; he disowns her, calling her his "sometime daughter." Kent speaks up in support of Cordelia and he too is banished.
Cordelia is true and logical. She even tries to show Lear that since Goneril and Regan are married and give a portion of love to their husbands, they can't possibly give Lear "all" of their love:
Why have my sisters husbands if they say
They love you all? (I.i.97-98)
Lear is too proud and shows poor judgment in not recognizing Cordelia's logic and in not recognizing Kent's wisdom.