This is why I can relate to Arthur so much! Because Uther's abuse isn't physical. He's not hitting his son, he's not shouting at him. And he does love his son.
But, there is this constant threat of failure hanging over Arthur's head.
He's constanly threatened to lose his position as crown prince, as Uther's SON due to Uther's mood swings.
Arthur's actions and morals are born from Uther's teachings, yet him following through with those actions disappoint his father and humiliate Arthur in front of him.
There is one scene that really hit me hard.
Arthur: "I always thought I was a huge disappointment to you!"
Uther: "That is my fault and not yours."
I love this scene because Uther acknowledges the fact that he's failing his son, but he never changes his behavior. Arthur, up to this point, has accepted the fact that he'll never be good enough. So, to hear that must have been such a fucked up feeling. Because it ties Arthur's hopes back to Uther and make him believe that it will change, that his father will accept him after all.
It's even worse because Uther is genuine in this scene. He doesn't realize how manipulative this is. I love this scene because it BREAKS me.
Arthur is EVERYTHING his father wanted him to be. He's basically the embodiement of Uther's dreams. The best fighter among the knights. He's noble, he's kind, he genuinely cares about Camelot, he even has his own mind, as Uther encourages him to have. He encourages and inspires the people, he speaks up at Injustice and works hard to bring Peace to Camelot. Arthur outgrows his own arrogance and becomes the ideal prince.
And yet... It's not enough. Because it's NEVER enough. Because Uther only has power over his son when Arthur makes mistakes, when he has to guide him. Arthur is the disappointment because Uther needs him to be that too.
And it shows a subconscious guilt on Uther's part. Because he knows why Arthur exists. Arthur is, in his war, the catalyst, as Uther's favorite mistake. I'm sure Uther loves Arthur, but he's also wary of him, fears him in a way. If Uther shows Arthur love, then I think, Uther would feel like he doesn't acknowledge his mistake. It's Uther's way of punishing himself.
I don't know if this is connected, but the harder Uther rages against magic, the colder he is towards his son.
And Arthur has to bear the brunt of it. To be everything he's meant to be. Including Uther's worst mistake.