When Kagome Higurashi travels back in time to Feudal Era Japan in Inuyasha, she meets her former reincarnation along with several ancestors of her classmates. Given the messy outcomes of time travel seen in other forms of popular media, viewers have come to expect certain repercussions for visiting the past. Despite this misconception, Kagome never became her own ancestor -- here's why.
While living at her family's Shinto shrine in modern-day Japan, Kagome is suddenly dragged into the Bone Eater's Well by a demon. After falling into the unsuspecting well, Kagome travels through time and finds herself in the Feudal Era where demons and the supernatural run rampant. Upon her arrival, she soon stumbles into Inuyasha who's bound to the sacred tree by an arrow. Inuyasha instantly mistakes Kagome's identity, yelling at her and calling her Kikyō despite Kagome correcting him multiple times. Kagome discovers Inuyasha is bound by a sacred arrow and spell cast upon him by the priestess Kikyō -- who happens to be her doppelgänger.
Upon Kagome's arrival in the past, she unknowingly awakens and captures the interest of the nearby surrounding demons. Inuyasha senses the Shikon Jewel inside Kagome, even though he last saw it with Kikyō after he was framed into stealing the sacred jewel and getting captured. Given Kagome and Kikyō's identical appearance and the fact that the Shikon Jewel was living inside Kagome, the series quickly confirms its young protagonist is Kikyō's reincarnation from the future. However, the Shikon Jewel is soon released and shattered into small shards that lead Kagome and Inuyasha to team up on a mission to find them.
Since Kagome is Kikyō's reincarnation, she has priestess abilities and can sense the Shikon Jewel shards whenever they're near by. This ability proves incredibly useful to the group's mission, and Kagome harnesses her priestess powers while learning archery similar to Kikyō's techniques. While it's clear Kagome and Kikyō have an undeniable bond and connected fates as reincarnations, Inuyasha never suggests or states they were blood relatives in any way. Furthermore, Kikyō dies before having any children or descendants, making it impossible for her to be in Kagome's direct lineage.
While Kagome doesn't encounter anyone verified to be her ancestor, she runs into the genuine ancestor of a classmate during her travels in the past. She unexpectedly meets Hōjō's direct ancestor, Akitoki, after seeing Hōjō's family tree at school that shows his ancestors were named Akitoki and Kagome. This frightens Kagome, who begins to question if she will get trapped in the Feudal Era and end up marrying Akitoki to become Hōjō's ancestor in a crazy twist of fate. These events are later proven a coincidence of names, however, as Kagome ultimately chooses to stay behind in the Feudal Era to marry Inuyasha and have a half-demon daughter.
While many Inuyasha fans believe Kagome becomes her own ancestor as a result of messy time travel, there is nothing in the series to indicate who Kagome's ancestors actually are. There are many fan theories, with some originally speculating Rin was her ancestor until it's later revealed she has children with Sesshomaru, which makes her descendants part-demon. Some fans even speculate that Miroku and Sango may be Kagome's ancestors since they don't have any demon bloodlines. Despite these intriguing possibilities, it is safe to say that Kagome is not her own ancestor.