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This idea is so dear to me! Because we see Arthur self-loathing so many times, both in relation to himself and his father's legacy, but it goes further beyond that.
There's a deleted scene from either "The Tears of Uther Pendragon" part one or two where Arthur is discussing Uther's descent into madness with Merlin. Arthur reveal's that Uther's father fell into a similar state later on in life, and Merlin "helpfully" points out that he learned from Gaius that those sorts of things tend to run in families. This leads to Arthur glaring at Merlin in anger at the accidental implication that Arthur himself would fall into a similar state of madness one day.
So, we can make a logical guess that Arthur, on some level, believes Pendragon blood to be cursed with madness and bloodlust. While it doesn't really come up again later in the series, we can assume that Morgana being revealed as Arthur's sister and becoming a tyrant only further solidifies this belief in Arthur.
To Arthur, he killed his own mother with his birth, having been born a murderer and trained form that day on to be the perfect warrior. To Arthur, he is damned by his own loyalty to slaughter as many people as it takes in the name of protecting his kingdom, and he's never known a single day in his life without blood on his hands.
And, on top of all of that, madness and tyranny runs through his blood, as evident from his father and half sister.
Arthur wants so very badly to be a good king, to be kind and protect his people, but he feels like he can never achieve that with all the lives he's taken and the evil that runs through his own blood. He could not carve out the part of himself he sees as rotten more than he could empty his own veins.
That's part of why Arthur is always so awed at Merlin's never-ending loyalty and kindness towards Arthur. Arthur sees himself as good for nothing except violence, and he does not know what to do with Merlin's soft care.
“something is rotten inside of me, i have to find it and cut it out” — house song; searows