To put it lightly, Tidus and Jecht did not have the best relationship. When Tidus was younger, he felt he had to compete with his father for his mother's attention. She was in love with Jecht, and ignored Tidus' calls when Jecht was around. Although his father sent his mother to him when he called, Tidus blamed his father for his mother's lack of attention.
When Tidus was still a child, Jecht disappeared at sea while practicing blitzball. Playing the game, we learn that Jecht was somehow taken to Spira, but the people in Zanarkand had no idea what had happened to Jecht. Search parties were set up to hunt for Tidus' father, and in the end, it was assumed that Jecht had died. Although Tidus was happy that Jecht was never found, Tidus' mother was beside herself with grief, and stopped living. She died shortly after Jecht was pronounced dead. I think Tidus blamed Jecht for his mother's death. He blamed Jecht for leaving.
In those ways, I think Tidus' mother was a major reason Tidus hated his father.
Growing up, Tidus felt overshadowed by his old man. Jecht was a famous Blitzball player. Following in his footsteps, Tidus had a lot to live up to. Jecht told Tidus that he would never be as a good as he is, and after Jecht went missing, Tidus set out to prove him wrong.
Jecht was arguably emotionally abusive to Tidus. He called Tidus names, he told him he wasn't good enough, and constantly cut him down. I think Jecht really loved his son, though. When Tidus was calling for his mother, and she put him off, Jecht told her to go to Tidus. In Jecht spheres and in flashbacks, it becomes clear how much Jecht really did love Tidus. He wanted Tidus to become a star blitzball player. He wanted Tidus to be taken care of. When Jecht realized he wouldn't be returning to his Zanarkand, he asked Auron to find a way to get to Tidus, and to take care of him.
Something else we learn in Jecht spheres is Jecht wasn't very good at expressing his emotions. I think he viewed emotions as weaknesses, but whatever the reason, he felt very uncomfortable telling Tidus how he felt. It was obvious he wanted to apologize to Tidus, and to tell him he loved him. He couldn't get it out, though.
I think picking on Tidus was Jecht's way of expressing love to his son. Although he said Tidus wouldn't be able to do it, Jecht showed Tidus the Jecht shot, something people paid to see. Although I think his way of thinking was flawed, I think he thought tough love would toughen Tidus up, so that he could reach his utmost potential. Whether Tidus would admit it himself or not, Tidus became a Blitzball star as a direct influence from his father. If Jecht was wanting to make Tidus the best, he succeeded.
In Spira, Tidus learned that his father was Sin. Jecht actually came to Dream Zanarkand to pick up Tidus. When Tidus was in contact with Sin, and every time he came in contact with Sin after, he felt his father. Auron told Tidus that Sin killed to come see Tidus. He said Jecht wanted Tidus to see what Sin did so that Tidus would kill him.
Tidus became so angry at Jecht not only for leaving him, but for causing so much pain and death in Spira. I think his anger turned to sadness and pity, though. Tidus spoke to Jecht after Sin passed, promising to end his pain.
After the party fights and defeats Sin, Jecht is dying, Tidus finds himself in tears over Jecht. I think he realized how much he really cared about his dad.
You know... for the first time, I'm glad... to have you as my father.
They loved each other. Fittingly, Tidus told Jecht he hated him.