Morgana has many reasons to hate Uther.
1) All her life, she has watched the executions of many magical users like her at the hand of Uther. He was willing to killing Mordred, a child she really cared about and Alvarr, who she had a kind of crush on. She knew that if he ever discovered she was a seer/sorceress, he would have her burned.
2) He lied to her all her life about Gorlois being her father, when in actual fact he was. He had an affair with her mother Vivienne and thus Morgana was conceived. Even when she basically told him she knew the truth, he denied her to her face. Being older, she believes she should be the rightful heir to the throne of Camelot. She also feels abandoned and upset about being lied to for her life.
3) He has grabbed her by the throat and locked her in his dungeons in chains. He has threatened her for doing what she believed right.
She has plenty of reasons and quite frankly, I believe she was pushed to the dark side by him.
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If you mean Morgana in BBC Merlin then she is his Ward. But in S3 we find out she is actually his daughter and not Gorlois'.
Guinevere was just Lady Morgana's maid when Uther was at the throne. Guinevere soon became close to Prince Arthur and when Arthur became King he choose Guinevere to be his Queen.
Merlin had a sort of "love at first sight" relationship in the beginning of Series 1 with Morgana that turned to a close friendship and then to a strained relationship after she tried to kill Uther. In Series 2 it appeared that Merlin and Morgana's relationship had been repaired and they shared deep feelings for one another, but Morgana began to slowly drift into isolation because of her confusion from her powers and her hatred of Uther. Yes, Merlin did poison Morgana, but it is clear on numerlous occasions that it was one of the hardest decisions (if not THE hardest) he's ever made. He didn't want to kill her, but he had no choice. In Series 3 they do become adversaries, but it is clear that Merlin feels guilty for how Morgana has changed to this villain, and he still appears to care for her.
Yes, Uther did.
Uther Pendragon, the King of England, was deeply in love with Igraine of Cornwall. Uther's assistant, Merlin, a magician, promised that they would be married if Uther gave Merlin a son. So, Uther and Igraine fell in love and had Arthur who was sent to live with Sir Ector for safety and because Uther was going to die.