Disclaimer: I don't own Merlin.
Arthur's relationship with Uther had always been strained. As a young boy, Arthur had always tried to please his father. He strove to be the best in sword fighting and riding horses. When it came to reading and writing, he did his best to excel in those as well, even if he didn't find them very interesting. He pushed himself hard so that he could be the best at everything. He wanted to prove to his father that he was worthy of being the prince of Camelot.
However, no matter how hard he tried, he could never live up to his father's expectations. In everything he did, his father always found fault. When his father watched him sword fight, he would constantly correct his stance. When his father checked on his writing skills, he always complained about his messy handwriting.
Arthur never gave up trying though. Whenever his father criticized him, he would push himself to work even harder. One day his efforts would pay off. One day, Uther would tell him that he was proud to call Arthur his son.