Disease and sickness are rare things in the world of Naruto, especially when it comes to important characters. Few characters are ever affected by a serious illness. Most end up perishing through combat or self-sacrifice. This raises a big question: why would Itachi Uchiha of all people be afflicted with a terminal disease that plays such a major factor in his death? The answer is that Itachi's illness may serve a larger purpose regarding the plot and his character.
Itachi is someone who often chooses to take on burdens so that others don't have to. For example, he takes on the burden of being an older brother, a ninja, a spy, a traitor and a martyr all in hopes of sparing other people from pain. Itachi attempts to single-handedly save the entire village and his brother without anyone else's help. All these responsibilities create a lot of stress and anxiety that wear on the body and weaken it. Even Itachi himself says that he attempted to do too many things on his own. When he is revived during the Fourth Shinobi War, he warns Naruto that attempting to do everything alone will lead to failure: "No matter how strong you become, don't try to bear the weight by yourself. You will fail. Don't forget about your friends."
For almost his entire existence, Itachi had to live a double life. He had to be a spy for the Leaf Village while pretending to be a spy for the Uchiha clan. He had to pretend to be a traitor to the Leaf Village while undercover in the Akatsuki. Itachi also had to pretend to be a monster who killed his own family for power when in reality, he loved them dearly. Itachi was never able to be his true self. Hiding his true intentions for most of his life added to the stress he was dealing with. It was only after his resurrection that Itachi was finally able to be who he really was.
However, all the stress, anxiety and turmoil that Itachi experienced during his life was never openly expressed. Even from a young age, Itachi never showed his emotions or allowed people in. This is shown when Itachi used to tap Sasuke on the forehead, creating distance between him and his brother. The emotional pain that came from killing his family, hurting Sasuke and lying about his true identity was never released in a healthy manner. All of these suppressed emotions couldn't be contained forever, so they manifested as his illness. Everything he wanted to say or express but couldn't was turned into a type of cancer that slowly poisoned him until his death.
During the Fourth Shinobi War, Itachi admits that he views his entire life as a failure. Not being honest with Sasuke about the Uchiha massacre was a mistake; he believes that if he had not tried to bear all of his burdens alone, everything would have turned out for the better. Tragically, if Itachi had lived his life honestly and not tried to hide his true feelings, it's possible that he would have never contracted his illness in the first place.
