The world of Jujutsu Kaisen is quite strict about its rules. While this makes for a relatively easy-to-understand power system and mostly straightforward battles, it can also make for awkward realizations when seemingly disconnected events line up a little too well. It's been established that the final words of many characters often contain a curse directed at the listener. This unique phenomenon gives deaths a lot more weight in the story and has led fans to believe that Wasuke Itadori’s final request may have inadvertently placed a curse on his grandson.
Yuuji was orphaned at a very young age and grew up with his grandfather as his sole guardian. The two were each other’s only family, and as a result, Yuuji was the only other person present at his deathbed. Before Wasuke drew his last breath, he placed a heavy burden on Yuuji, giving a lengthy speech that essentially charged him with saving and helping as many people as he could.
This seems a fairly innocent request, but the sequence of events that follow paints that final request in a more sinister light. Almost immediately after his grandfather's death, Yuuji ran into Fushiguro for the first time. After learning the nature of Fushiguro's mission and the potential danger his senpai faced, Yuuji was uncharacteristically frightened. He was pushed to act upon remembering his grandfather's words, and the rest, as they say, is history; he ended up swallowing Sukuna's finger.
Swallowing the special-grade cursed object may have been the only way Itadori could save those around him but it also ended up putting a massive target on his back. The elders in jujutsu society believed him to be a half-cursed monster and ordered his execution. It was only through Gojo Satoru's intervention that his death was delayed. In return, Yuuji agreed to search for and ingest all of Sukuna's other fingers. His execution was suspended until all 19 other fingers were collected. Essentially, Yuuji is living on borrowed time.
Yuuji has actually referenced his grandfather's final words on one occasion, calling saving those in need his "troublesome curse." While in that situation, he meant it figuratively, there's a theory that his task is a more literal curse. Given how his life was turned around after he acted on it for the first time, this might just be true.
Itadori's time as a jujutsu sorcerer has been fraught with recurring dangers and unimaginable losses. To survive, he's committed several acts that leave him questioning whether or not his moral compass is still pointed in the right direction. Moreover, he still needs to contend with the looming threat of his execution and being treated like an outcast by much of jujutsu society. It's a thankless job with no upsides save for the few friends he's made at Jujutsu High -- truly an existence worthy of being called a curse.
