Lear is motivated by love for his daughters and his reactions to their apparent love or lack of it for him. Time and again, and increasingly as the play progresses, all three daughters let him down, to his way of thinking. The progression of his madness is exacerbated not only by the emotional damage that this lack of love causes him, but by the physical effects of being shut out onto the moor.
As he reacts to their actions and his view that they are being unreasonable--such as in refusing to allow the full complement of his men to accompany him--he rants and rails against them. He calls for dreadful curses such as barrenness to attack them.
It is easy to see all these things as indications that Lear hates his daughters. But it is also possible to understand his motivations from the other perspective. Lear does not hate his daughters; he loves them too much. His madness progresses in large part from his realization that they are unworthy of his love. He refuses to believe they have rejected him: "They could not, would not do 't; 'tis worse than murder." It is when he understands that this rejection is complete that his heart breaks as he sees that his very sanity is in danger.
No, I'll not weep:
I have full cause of weeping; but this heart
Shall break into a hundred thousand flaws,
Or ere I'll weep. O fool, I shall go mad!
In sum, Lear loves his daughters. The realization that his love has led him astray, including that Cordelia alone reciprocated his love, is what ultimately breaks and then kills him.