Keep in mind that she was Uther's ward for most of her life, and was repeatedly taught that magic was "evil". She was able to witness first-hand Uther's tyranny against magic - brutal executions, man-hunts etcetera. That being said she did not agree with Uther's decisions. We see in the very first episode (S1E1) that she tried to persuade Uther to not execute Thomas Collins, a magician.
And then she realises she herself can use magic, and the dangerous predicament this puts her in. Merlin immediately packs her off to the Druids, where her belief that magic can be used for good is strengthened during her stay there. She hates that she has to hide her magic because of Uther, furthermore knowing for a fact that she is not "evil", yet will be executed all the same if he found out.
Finally this reaches the tipping point after she is abducted by Morgause, who does the opposite of what Uther has been doing - accepting Morgana for what she is, a magician. She's not alone anymore.
“I don't want to be brave. I just want to be myself. I don't want to be alone anymore.”
And with that in mind, she fully realises Uther has always been wrong about magic and grows to hate him even more. She wants to rid Camelot of Uther, and Arthur, who she believes is just like his father, so that magicians all around won't be persecuted there again.
Her final turning point is after Merlin attempts to poison her (making her feel betrayed) and her 1 year long "captivity" with Morgause which was ample time for her hatred of Uther (and Arthur) to grow even further.