Right from the beginning, we can see that Morgana is against the way that magicians are treated. Her very first scene shows her disagreeing with Uther over the public execution of a man, and telling him that the anniversary of a genocide is nothing to be celebrated. This becomes a running theme through the first season or so, with Morgana standing up to Uther. Now, Uther responds in a variety of ways, ranging from having her removed by guards to chaining her in a cell (he also fails to mention that she is his daughter, lying about her parantage and depriving her of her rightful place in line of the throne).
Fast forward a year or so. She had been having night terrors her whole life, but they are starting to get worse. Morgana begins to realise that she has magic, but she has no idea how to handle this. She is living under the roof of the man who has killed countless people of her kind, and she can't tell anyone for fear of her secret getting out. Enter Gaius , her physician since childhood. He suspected the whole magic thing, but rather than talk to her about it, he decides to drug her in the hopes of keeping her magic suppressed. Now, I understand that he means well, but the fact that he has been giving her strong drugs since an early age without her informed consent makes me feel really uncomfortable.
During all of this time, she has become a close friend of Merlin's. Now, he knows exactly what is going on with Morgana. Rather than try to help her deal with this, he decides to try and kill her after a very brief conversation with a dragon. He barely protests, and a little later, we see him slip hemlock into her drink and then force her into an embrace as her lungs paralyse and she starts to suffocate (the show then decides to focus on his emotional pain in this situation, rather than the fact that she is terrified, in pain and dying). Merlin also commits various other horrible acts against her, such as pushing her down the stairs ad bashing her skull in against walls.
Before moving on, I’d also like to draw attention to her reason for turning against Arthur. Although he doesn't do anything against her outright, he stands by as Uther commits various acts of abuse against her and does nothing. Also, we later find out that he took part in the murder of magical people, which doesn't exactly act in favour of her view on him.
Now, from this, we can draw the conclusion that Morgana has no one she can trust. She is living under the same roof as a genocidal dictator, and she wants nothing more than to bring him down so that magic can be restored. In comes Morgause, a woman who was nearly killed as a child during one of Uther's rampages, and also happens to be Morgana's sister. Now, unlike every other character in the show, Morgause decided to help Morgana. Not only does she give Morgana a bracelet to stop her dreams, she also offers her something Morgana has been wanting for a long time: a chance to bring down Uther. Just as they are about to succeed in this, Merlin slips Morgana the poison. Now, Morgause could have left her to die. They'd only known each other for a very short period of time, and Morgause's life-long ambition seems to have been to get rid of Uther. However, she abandons all of that in favour of saving Morgana, who has never had anyone show that kind of commitment to her before.
Then, a few seasons later, Merlin smashes Morgause's head in against a wall (which for some reason means that half of her body starts rotting... I don't even know what was going on here). This eventually led to Morgause's death, which kind of pushed Morgana over the edge (I'd like to point out that most of that season was about Morgana trying to bring Morgause back, but Emilia fox decided not to return, meaning they had to cut her scenes out, and thereby making it look like Morgana was acting without motive. She wasn't.)
And, as the end of the last season/the start of this season added : multiple stabbings, more being thrown against walls, and two full years of torture, followed by more night-terrors (though these ones are induced by PTSD rather than magic) and yet another betrayal, this time by Mordred. I don't even want to go into this too much, she seems to be driven by a combination of revenge and trauma at the moment, and it just makes me really sad that the show decided to put her through all of this.
I've left quite a bit out, mainly because I reeeaally need to get back to my homework now and also because I can't remember everything I want to say without looking stuff up, but I'd like to conclude here. Although I don't agree with everything she has done, I think that her goal is much more admirable than Merlin's (who spent 4 seasons defending someone who has killed so many people) and I think that the fact that she is still standing after all of the lies, abuse, manipulation, loss of loved ones, betrayals and trauma makes her the strongest character of the show.
(This doesn't mean that I support her every action. Her resent treatment of Gwen is terrible, as was the firing of arrows at the crowd and burning the crops. However, this isn't anything worse than the multitude of murders committed by Arthur, Merlin and Uther, and I feel that the way her actions are highlighted whilst theirs is swept aside is unfair)