What's with paradoxes?

 Hello again anime lovers of the world! have you ever seen an anime paradox before? That's when something in the anime completely contradicts another thing. I glad to say that i know quite a few of them! this is directed to all you guys  and girls who know the anime Inuyasha. As you should know this already, Kikyo is apparently Kagome's anscetor right. But in the anime, Kikyo dies near the finale, so wouldn't Kagome have ceased to exist? But apparently she saves her own existence by living with Inuyasha in the past and becoming her own ancestor. What's up with that?